The Buser inequality is a reverse Cheeger inequality in case of non-negative Ricci curvature stating that λ 1 ≤ C h 2 where λ 1 is the smallest positive eigenvalue of the Laplacian, and h is the Cheeger constant, and C is a constant, see Theorem 3.2.2.Poincaré-Sobolev-type inequalities indisputably play a prominent role not only in the theory of Sobolev spaces but also in a wide range of applications in analysis of partial differential equations, calculus of variations, mathematical modeling or harmonic analysis (e.g. [5, 20, 44]).These types of inequalities have been exhaustively studied for decades and have been generalized in many ...Mar 23, 2022 · Matteo Levi, Federico Santagati, Anita Tabacco, Maria Vallarino. We prove local Lp -Poincaré inequalities, p ∈ [1, ∞], on quasiconvex sets in infinite graphs endowed with a family of locally doubling measures, and global Lp -Poincaré inequalities on connected sets for flow measures on trees. We also discuss the optimality of our results. 数学中，庞加莱不等式（英語： Poincaré inequality ）是索伯列夫空间理论中的一个结果，由法国 数学家 昂利·庞加莱命名。 这个不等式说明了一个函数的行为可以用这个函数的变化率的行为和它的定义域的几何性质来控制。 也就是说，已知函数的变化率和定义域的情况下，可以对函数的上界作出估计。his Poincare inequality discussed previously [private communication]. The conclusion of Theorem 4 is analogous to the conclusion of the John-Nirenberg theorem for functions of bounded mean oscillation. I would like to thank Gerhard Huisken, Neil Trudinger, Bill Ziemer, and particularly Leon Simon, for helpful comments and discussions. NOTATION.The sharp Sobolev type inequalities in the Lorentz-Sobolev spaces in the hyperbolic spaces. Journal of Mathematical Analysis and Applications, Vol. 490, Issue. 1, p. 124197. Journal of Mathematical Analysis and Applications, Vol. 490, Issue. 1, p. 124197.In this paper, a simplified second-order Gaussian Poincaré inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a general Rademacher functional and a Gaussian random variable, which is established by means of the discrete Malliavin-Stein method and is of independent ...examples which show that this inequality is false for all p < 1, even if q is very small, Ω is a ball, and u is smooth (one such example is given near the end of Section 1). Nevertheless, we shall show that, under a rather mild condition on ∇u, one can prove such an inequality in any John domain for all 0 < p < 1 (see Theorem 1.5).We show that Poincaré inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains. Keywords. 46E35 reverse doubling weights Poincaré inequality John domains. TypeMoreover, if a p-logarithmic Sobolev inequality holds then the Poincaré inequality is shown to hold too, therefore the previous regularization result is valid. Finally, the weighted Sobolev-type inequality ‖ u ‖ q ⩽ C E (p) (u) (q < p) implies L q 0 - L ϱ regularization of the evolution for any ϱ < ϱ ˜, all q 0 < ϱ ˜ and an ...For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincare inequality for p > Q in terms of the p-modulus of quasiconvex curves connecting pairs of points in the space. A related ...Lipschitz Domain. Dyadic Cube. Bound Lipschitz Domain. Common Face. Uniform Domain. We show that fractional (p, p)-Poincaré inequalities and even fractional Sobolev-Poincaré inequalities hold for bounded John domains, and especially for bounded Lipschitz domains. We also prove sharp fractional (1,p)-Poincaré inequalities for s-John …The relationship between Lyapunov conditions and functional inequalities of Poincaré type (or- dinary or weak Poincaré introduced in [24]) is studied in details in the recent work [3]. The present paper is thus a complement of [3] for the study of stronger inequalities than Poincaré inequality. Let us also mention the paper [2] which is a ...1 Answer. Finding the best constant for Poincare inequality (or korn's inequality) is a long standing problem. Unfortunately, there is no general answer. (not I am known of). However, for some specially domains, there is something you can do. For example, if Ω Ω is a ball, then the best constant is the radius of the ball (or something similar).The doubling condition and the Poincar e inequality are relatively standard assumptions in analysis on metric measure spaces. There are several phenomena in harmonic analysis and PDEs for which a (q;p ")-Poincar e inequality for some ">0 would be a more natural assumption than a (q;p)-Poincar e inequality. This isThe Poincaré, or spectral gap, inequality is the simplest inequality which quantifies ergodicity and controls convergence to equilibrium of the semigroup P = ( P t ) t≥0 towards the invariant measure μ (in other words, the convergence of the kernels p t ( x, dy ), x ∈ E, as t →∞, towards dμ ( y )).The latter inequality allows us to recover by different techniques some weighted Poincaré inequalities previously established in Bobkov and Ledoux [12] for the Beta distribution or in Bonnefont, Joulin and Ma [14] for the generalized Cauchy distribution and to highlight new ones, considering for instance Pearson's class of distributions.Cheeger, Hajlasz, and Koskela showed the importance of local Poincaré inequalities in geometry and analysis on metric spaces with doubling measures in [9, 15].In this paper, we establish a family of global Poincaré inequalities on geodesic spaces equipped with Borel measures, which satisfy a local Poincaré inequality along with …This example shows that the super-Poincare inequality and the Nash-type inequality can be satisfied by a generator but without ultracontractivity of the corresponding semigroup. 4.2 The Riemannian setting. Let \(M\) be a connected complete Riemannian manifold with Ricci curvature bounded below.Function approximation and recovery via some sampled data have long been studied in a wide array of applied mathematics and statistics fields. Analytic tools, such as the Poincaré inequality, have been handy for estimating the approximation errors in different scales. The purpose of this paper is to study a generalized Poincaré inequality, where the measurement function is of subsampled type ...We show that unbounded John domains (and even a larger class of domains than John domains) satisfy the weighted Poincar(cid:19)e inequality inf a 2 R k u ( x ) − a k L q ( D,w 1 ) (cid:20) C kr u (…Poincare type inequality is one of the main theorems that we expect to be satisfied (and meaningful) for abstract spaces. The Poincare inequality means, roughly speaking, that the ZAnorm of a function can be controlled by the ZAnorm of its derivative (up to a universal constant). It is well-known that the Poincare inequality implies the SobolevIf this is not the inequality that you want, I'd suggest making another question in order to avoid confusing edits. $\endgroup$ - Jose27 Sep 25, 2021 at 9:10Abstract. L p Poincaré inequalities for general symmetric forms are established by new Cheeger's isoperimetric constants. L p super-Poincaré inequalities are introduced to describe the ...Aug 31, 2017 · Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. AN OPTIMAL POINCARE INEQUALITY IN L1 FOR CONVEX DOMAINS GABRIEL ACOSTA AND RICARDO G. DURAN (Communicated by Andreas Seeger) Abstract. For convex domains ˆRnwith diameter dwe prove kuk L1(!) d 2 kruk L1(!) for any uwith zero mean value on!. We also show that the constant 1=2in this inequality is optimal. 1. Introduction Given a bounded domainIn this paper, a simplified second-order Gaussian Poincaré inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a general Rademacher functional and a Gaussian random variable, which is established by means of the discrete Malliavin-Stein method and is of independent ...6. Poincaré inequality is given by. ∫Ωu2 ≤ C∫Ω|∇u|2dx, ∫ Ω u 2 ≤ C ∫ Ω | ∇ u | 2 d x, where Ω Ω is bounded open region in Rn R n. However this inequality is not satisfied by all the function. Take for example a constant function u = 10 u = 10 in some region. Happy to have have some discussions about it. Thanks for your help.Poincaré inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis Christophe Andrieu, Anthony Lee, Sam Power, Andi Q. Wang School of Mathematics, University of Bristol August 11, 2022 Abstract We develop a theory of weak Poincaré inequalities to characterize con-vergence rates of ergodic Markov chains.In view of our discussion of the Dirichlet integral, we call Inequality ♦ weak Hardy inequality if ker q ={0} and weak Poincaré inequality if ker q ={0}. In the case = 0, the function α becomes a constant and Inequality ♦is referred to as Hardy inequality if ker q ={0}, respectively Poincaré inequality if ker q ={0}.The aim of this paper is to prove a Poincare type \(p-q\) inequality in a homogeneous space \((\mathbb {R}^N, d, \mu ) \) estimating weighted Lebesgue norm …For generators of Markov semigroups which lack a spectral gap, it is shown how bounds on the density of states near zero lead to a so-called weak Poincaré inequality (WPI), originally introduced by Liggett (Ann Probab 19(3):935–959, 1991). Applications to general classes of constant coefficient pseudodifferential operators are studied. Particular examples are the heat semigroup and the ...Nobody has time to read an 80 page paper [LE20]. Therefore I doubt most readers realized the manifold Langevin algorithm paper actually contains a novel technique for establishing functional inequalities. And I really doubt anyone had time to interpret the intuitive consequences of such results on perturbed gradient descent, and definitely not …We show that Poincaré inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains. Keywords. 46E35 reverse doubling weights Poincaré inequality John domains. Type1. (1) This inequality requires f f to be differentiable everywhere. (2) With that condition, the answer is the linear functions. The challenge is to prove that. (3) You might as well assume n = 1: n = 1: larger values of n n are trivial generalizations because both sides split into sums over the coordinates.energy side of the Poincare´ inequality. In particular, our results apply to geodesic balls in ideal sub-Riemannian manifolds, such as the Heisenberg group. Mathematics Subject Classification (2010): 35P15 (primary); 58J50, 53C23, 51F99 (secondary). 1. I ntr oduc i Determining the optimal constant in the Poincar´e inequality, which in an ...But the most useful form of the Poincaré inequality is for W1,p/{constants} W 1, p / { c o n s t a n t s }. This inequality measures the connectivity of the domain in a subtle way. For example, joining two squares by a thin rectangle, we get a domain with very large Poincaré constant, because a function can be −1 − 1 in one square, +1 + 1 ...Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces. Kaushik Bal, Kaushik Mohanta, Prosenjit Roy, Firoj Sk. We provide sufficient conditions for boundary Hardy inequality to hold in bounded Lipschitz domains, complement of a point (the so-called point Hardy inequality), domain above the graph of a Lipschitz function, …Aug 11, 2021 · In this paper, a simplified second-order Gaussian Poincaré inequality for normal approximation of functionals over infinitely many Rademacher random variables is derived. It is based on a new bound for the Kolmogorov distance between a general Rademacher functional and a Gaussian random variable, which is established by means of the discrete Malliavin-Stein method and is of independent ... What kind of Poincare inequality is that, in which the derivative lies on the left hand-side? Is $\partial_X^{-1} B$ the inverse derivative of B or what? Is there any way, one can modify the classical Poincare inequality (see Evans, PDEs, §5.8) using Fourier transform in order to obtain something similar to this?In this paper, we prove a sharp lower bound of the first (nonzero) eigenvalue of Finsler-Laplacian with the Neumann boundary condition. Equivalently, we prove an optimal anisotropic Poincaré inequality for convex domains, which generalizes the result of Payne-Weinberger. A lower bound of the first (nonzero) eigenvalue of Finsler-Laplacian with the Dirichlet boundary condition is also proved.A NOTE ON POINCARE- AND FRIEDRICHS-TYPE INEQUALITIES 5 3. Poincar e-type inequalities in Hm() Now we consider Poincar e-type inequalities in Hm() with m2N 0. Throughout this section let ˆRdbe a bounded domain with Lipschitz boundary. On Hm() we use the inner product (u;v) m= X jsj m Z DsuDsvdx and the induced norm kkmod03lec07 The Gaussian-Poincare inequality. NPTEL - Indian Institute of Science, Bengaluru. 180 08 : 52. Poincaré Conjecture - Numberphile. Numberphile. 2 30 : 29. Lecture 15 (Part 2): Proof of Poincare inequality, Existence and Uniqueness for Possion problem. Sukkur IBA University- Mathematics. 1 ...So basically, I have proved the Poincare's inequality for p = 1 case. That is, for u ∈ W 1, 1 ( Ω), I have | | u − u ¯ | | L 1 ≤ C | | ∇ u | | L 1. Here u ¯ is the average of u on Ω. Now I need to get the general p case, i.e., for u ∈ W 1, p ( Ω), there is | | u − u ¯ | | L p ≤ C | | ∇ u | | L p. My professor in class ...In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition.Scott Winship is one of the most prominent academic skeptics of the idea that rising inequality is harming the American economy. Scott Winship started his career as a moderate Democrat, believing in progressive solutions to the US’s economi...We characterize complete RNP-differentiability spaces as those spaces which are rectifiable in terms of doubling metric measure spaces satisfying some local (1, p)-Poincaré inequalities. This gives a full characterization of spaces admitting a strong form of a differentiability structure in the sense of Cheeger, and provides a partial converse to his theorem. The proof is based on a new ...norms on both sides of the inequality is quite natural and along the lines of the results for improved Poincaré inequalities involving the gradient found in [7, 8, 14, 22], we believe that the only antecedent of these weighted fractional inequalities is found in [1, Proposition 4.7], where (1.6) is obtained in a star-shaped domain in the caseThe aim of this paper is to study (regional) fractional Poincaré type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results on regional fractional inequality are established depending on various conditions on domains and on the range of $ s \in (0,1) $. The best constant in both regional fractional and fractional Poincaré ...The main contribution is the conditional Poincar{\'e} inequality (PI), which is shown to yield filter stability. The proof is based upon a recently discovered duality which is used to transform the nonlinear filtering problem into a stochastic optimal control problem for a backward stochastic differential equation (BSDE).Lecture Five: The Cacciopolli Inequality The Cacciopolli Inequality The Cacciopolli (or Reverse Poincare) Inequality bounds similar terms to the Poincare inequalities studied last time, but the other way around. The statement is this. Theorem 1.1 Let u : B 2r → R satisfy u u ≥ 0. Then | u| ≤2 4 2 r B 2r \Br u . (1) 2 Br First prove a Lemma.The Poincaré inequality for the domain on the sphere (see e.g. Theorem 3.21 [145]). Let u ∈ W 1 (Ω) and Ω is convex domain on the unit sphere S N -1 . Then || u − …Abstract. In order to describe L2 -convergence rates slower than exponential, the weak Poincaré inequality is introduced. It is shown that the convergence rate of a Markov semigroup and the corresponding weak Poincaré inequality can be determined by each other. Conditions for the weak Poincaré inequality to hold are presented, which are easy ...Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack ExchangeA NOTE ON WEIGHTED IMPROVED POINCARÉ-TYPE INEQUALITIES 2 where C > 0 is a constant independent of the cubes we consider and w is in the class A∞ of all Muckenhoupt weights. The authors remark that, although the A∞ condition is assumed, the A∞ constant, which is defined by (1.3) [w]A∞:= sup Q∈QHelp Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products.1 Answer. Sorted by: 5. You can duplicate the usual proof of Hardy type inequalities to the discrete case. Suppose {qn} { q n } is an eventually 0 sequence (you can weaken this to limn→∞ n1/2qn = 0 lim n → ∞ n 1 / 2 q n = 0 ). Then by telescoping you have (all sums are over n ≥ 0 n ≥ 0)Regarding the Poincare inequality, I suppose it's a question of terminology. What do you take as your definition of Poincare's inequality? For what it's worth, I'm looking at the book and Evans writes "This estimate is sometimes called Poincare's inequality." (Page 282 in the second edition.)1 Answer. Sorted by: 5. You can duplicate the usual proof of Hardy type inequalities to the discrete case. Suppose {qn} { q n } is an eventually 0 sequence (you can weaken this to limn→∞ n1/2qn = 0 lim n → ∞ n 1 / 2 q n = 0 ). Then by telescoping you have (all sums are over n ≥ 0 n ≥ 0)Lecture Five: The Cacciopolli Inequality The Cacciopolli Inequality The Cacciopolli (or Reverse Poincare) Inequality bounds similar terms to the Poincare inequalities studied last time, but the other way around. The statement is this. Theorem 1.1 Let u : B 2r → R satisfy u u ≥ 0. Then | u| ≤2 4 2 r B 2r \Br u . (1) 2 Br First prove a Lemma. The sharp Sobolev type inequalities in the Lorentz-Sobolev spaces in the hyperbolic spaces. Journal of Mathematical Analysis and Applications, Vol. 490, Issue. 1, p. 124197. Journal of Mathematical Analysis and Applications, Vol. 490, Issue. 1, p. 124197.Mathematics. 1984. 195. The weighted Poincare inequalities in weighted Sobolev spaces are discussed, and the necessary and sufficient conditions for them to hold are given. That is, the Poincare inequalities hold if, and only if, the ball measure of non-compactness of the natural embedding of weighted Sobolev spaces is less than 1.THE UNIFORM KORN - POINCARE INEQUALITY´ IN THIN DOMAINS L’INEGALIT´ E DE KORN - POINCAR´ E´ DANS LES DOMAINES MINCES MARTA LEWICKA AND STEFAN MULLER¨ Contents 1. Introduction 2 2. The main theorems 4 3. Remarks and an outline of proofs 6 4. An example where the constant Ch blows up 8 5. An approximation of ∇u 10 6. The key estimates 12 7.Every graph of bounded degree endowed with the counting measure satisfies a local version of Lp-Poincaré inequality, p ∈ [1, ∞]. We show that on graphs which are trees the Poincaré constant grows at least exponentially with the radius of balls. On the other hand, we prove that, surprisingly, trees endowed with a flow measure support a global version of Lp-Poincaré inequality, despite ...of finite area, the analytic Poincare inequality (1.5) is equivalent to (1.6) for p = 2. Therefore, the Axler-Shields question is answered by our main results: Theorem 1. If D c Rd is a Holder domain, then D is a p-Poincare domain for all p > d. Theorem 2. If a domain D is a Holder domain, then (1.7) f kp(xo, x)dx < 0 D for all p < 00.Poincare (Wirtinger) Inequality vanishing on subset of boundary? 0. Explaining the Proof of Schwarz Inequality for Scalar Product in a Vector Space. 1. Explain Proof of Convergence of Matrix when Spectral Radius Less than 1. 1. Question about the proof of the Poincaré inequality. 1.This paper aims at proving new multipolar Hardy inequalities on negatively curved manifolds. To introduce the subject, let us recall the simplest form of the unipolar Hardy inequality on Riemannian manifolds, which is due to Carron [].If \((\mathcal {M},g)\) is an \(N\ge 3\) dimensional Cartan-Hadamard manifold, \(\mathrm{d}(., .)\) is the geodesic distance and \(x_0 \in \mathcal {M}\), the ...First, I consider the condition that $ \Omega $ is convex and prove the inequality. Now I want to deal with the general case by using the extension theorem of Sobolev space. ... Using the Rellich-Kondrachov theorem to prove Poincare inequality for a function vanishing at one point. 0. Poincaré inequality on annular regions. 4. A Poincaré-type ...We prove that complete Riemannian manifolds with polynomial growth and Ricci curvature bounded from below, admit uniform Poincaré inequalities. A global, uniform Poincaré inequality for horospheres in the universal cover of a closed, n -dimensional Riemannian manifold with pinched negative sectional curvature follows as a corollary. Comments:Matteo Levi, Federico Santagati, Anita Tabacco, Maria Vallarino. We prove local Lp -Poincaré inequalities, p ∈ [1, ∞], on quasiconvex sets in infinite graphs endowed with a family of locally doubling measures, and global Lp -Poincaré inequalities on connected sets for flow measures on trees. We also discuss the optimality of our results.Poincare inequality together with Cauchy-Schwarz. Ask Question Asked 1 year, 11 months ago. Modified 1 year, 11 months ago. Viewed 68 times 0 $\begingroup$ Given the advection ...Jules Henri Poincaré (UK: / ˈ p w æ̃ k ɑːr eɪ /, US: / ˌ p w æ̃ k ɑː ˈ r eɪ /; French: [ɑ̃ʁi pwɛ̃kaʁe] ⓘ; 29 April 1854 - 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed ...Poincaré-Korn type inequalities, in a vector-valued setting, are provided in [40,41,42,38]. For versions of (5) with a general 1 < p < ∞, we refer to [9,42, 44, 45]. While this yields a ...Poincaré inequalities for Markov chains: a meeting with Cheeger, Lyapunov and Metropolis Christophe Andrieu, Anthony Lee, Sam Power, Andi Q. Wang School of Mathematics, University of Bristol August 11, 2022 Abstract We develop a theory of weak Poincaré inequalities to characterize con-vergence rates of ergodic Markov chains.We show that any probability measure satisfying a Matrix Poincaré inequality with respect to some reversible Markov generator satisfies an exponential matrix concentration inequality depending on the associated matrix carré du champ operator. This extends to the matrix setting a classical phenomenon in the scalar case. Moreover, the proof gives rise to new matrix trace inequalities which ...The fact that a Poincaré inequality implies dimension-free exponential concentration for Lipschitz functions has a long history, dating back to work by Gromov ...New inequalities are obtained which interpolate in a sharp way between the Poincaré inequality and the logarithmic Sobolev inequality for both Gaussian measure and spherical surface measure. The classical Poincaré inequality provides an estimate for the first nontrivial eigenvalue of a positive self-adjoint operator that annihilates constants. For the …"Poincaré Inequality." From MathWorld --A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PoincareInequality.html Subject classifications Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d.Let Omega be an open, bounded, and connected subset of R^d for some d and let dx denote d-dimensional Lebesgue measure on R^d. In functional analysis, the Friedrichs inequality says that there exists a constant C such that int_Omegag^2(x)dx<=Cint_Omega|del g(x)|^2dx for all functions g in the Sobolev space H_0^1(Omega) consisting of those functions in L^2(Omega) having zero trace on the ...www.imstat.org/aihp Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 2013, Vol. 49, No. 1, 95-118 DOI: 10.1214/11-AIHP447 © Association des ...More precisely, we prove in Theorem 1.4 a matrix Poincare inequality for any homogeneous probability measure on the n-dimensional unit cube satisfying a form of negative dependence known as the stochastic covering property (SCP). Combined with Theorem 1.1, this implies a corresponding matrix exponential concentration inequality.This paper aims at proving new multipolar Hardy inequalities on negatively curved manifolds. To introduce the subject, let us recall the simplest form of the unipolar Hardy inequality on Riemannian manifolds, which is due to Carron [].If \((\mathcal {M},g)\) is an \(N\ge 3\) dimensional Cartan-Hadamard manifold, \(\mathrm{d}(., .)\) is the geodesic distance and \(x_0 \in \mathcal {M}\), the ...Apr 13, 2018 at 2:08. The previous link refers to the case ∞. For the case 1 n 1, see Brezis book. – Pedro. Apr 13, 2018 at 2:20. In general any inequality bounding the Lp L p norm …Poincaré inequality. Download conference paper PDF. 1 Introduction. This paper deals with (weak) Hardy/Poincaré inequalities for certain quadratic forms. First …Overall, the strategy of the proof is pretty similar to the one used in the proof of Theorem 3.20 in the aforementioned monograph, where a Gaussian Poincare inequality is demonstrated. I welcome any other approaches as well (either functional-analytic approach or geometric approach)!If this is not the inequality that you want, I'd su, A GENERALIZED POINCARE INEQUALITY FOR GAUSSIAN MEASURES WILLIAM BECKNER (Communicated by J. Marshall Ash) ABSTRACT. Ne, Sobolev and Poincare inequalities on compact Riemannian manifolds. Let M M be , WEIGHTED POINCARE INEQUALITY AND THE POISSON EQUATION 5´ as (1.5) for each annulus. However, instead of, For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincare inequality for , inequality with constant κR and a L1 Poincar´e inequality with constant ηR. A very bad bound for these co, This paper is devoted to the study of fractional (q, p)-Sobolev-Poincaré in- equalities in irregular domains. In , A NOTE ON SHARP 1-DIMENSIONAL POINCAR´E INEQUALITIES 2, $\begingroup$ It seems to me that the Poincare inequalit, general conditions for reverse poincare inequality. 4. Bound impr, Poincar´e inequality, this paper studies the weaker O, The only reference for inequalities of Poincare type on puncture, The main contribution is the conditional Poincar{\, Mar 20, 2006 · A NOTE ON SHARP 1-DIMENSIONAL POINCAR´E INEQUALITIES 2, Aug 15, 2022 · 1. (1) This inequality requires f f to be differ, The Li-Yau inequality is the estimate Δlnu ≥ − n 2t. Here u: M ×, In this paper, we prove capacitary versions of the frac, Poincar´e inequalities play a central role in the study of regularity.