scholarly journals Corrigendum to “Poincaré inequalities and Newtonian Sobolev functions on noncomplete metric spaces” [J. Differ. Equ. 266 (2019) 44–69]

2021 ◽  
Vol 285 ◽  
pp. 493-495
Author(s):  
Anders Björn ◽  
Jana Björn
Keyword(s):  
Metric Spaces ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Sobolev Functions

scholarly journals Poincaré inequalities, embeddings, and wild groups

2011 ◽  
Vol 147 (5) ◽  
pp. 1546-1572 ◽  
Author(s):  
Assaf Naor ◽  
Lior Silberman
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Isometric Action ◽  
Metric Embedding ◽  
Random Group ◽  
Cartesian Products ◽  
Poincaré Inequalities ◽  
Embedding Theory ◽  
Geometric Conditions ◽  
Poincare Inequalities

AbstractWe present geometric conditions on a metric space (Y,dY) ensuring that, almost surely, any isometric action onYby Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov–Hausdorff limits, and Cartesian products. We use methods from metric embedding theory to establish the validity of these conditions for a variety of classes of metric spaces, thus establishing new fixed point results for actions of Gromov’s ‘wild groups’.

Poincaré inequalities for linearizations of very fast diffusion equations

Nonlinearity ◽  
2002 ◽  
Vol 15 (3) ◽  
pp. 565-580 ◽  
Author(s):  
J A Carrillo ◽  
C Lederman ◽  
P A Markowich ◽  
G Toscani
Keyword(s):  
Diffusion Equations ◽  
Fast Diffusion ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Fast Diffusion Equations

scholarly journals ORLICZ–POINCARÉ INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 529-543 ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Porous Media ◽  
Probability Measure ◽  
Poincaré Inequality ◽  
Dirichlet Forms ◽  
Sobolev Inequalities ◽  
Young Function ◽  
Poincare Inequality ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Porous Media Equations

AbstractCorresponding to known results on Orlicz–Sobolev inequalities which are stronger than the Poincaré inequality, this paper studies the weaker Orlicz–Poincaré inequality. More precisely, for any Young function $\varPhi$ whose growth is slower than quadric, the Orlicz–Poincaré inequality$$ \|f\|_\varPhi^2\le C\E(f,f),\qquad\mu(f):=\int f\,\mathrm{d}\mu=0 $$is studied by using the well-developed weak Poincaré inequalities, where $\E$ is a conservative Dirichlet form on $L^2(\mu)$ for some probability measure $\mu$. In particular, criteria and concrete sharp examples of this inequality are presented for $\varPhi(r)=r^p$ $(p\in[1,2))$ and $\varPhi(r)= r^2\log^{-\delta}(\mathrm{e} +r^2)$ $(\delta>0)$. Concentration of measures and analogous results for non-conservative Dirichlet forms are also obtained. As an application, the convergence rate of porous media equations is described.

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