scholarly journals Poincaré Inequalities for Composition Operators withLφ-Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ru Fang
Keyword(s):  
Projection Operator ◽  
Composition Operators ◽  
Exterior Derivative ◽  
Derivative Operator ◽  
Poincaré Inequalities ◽  
Homotopy Operator ◽  
Poincare Inequalities ◽  
Harmonic Equation ◽  
Poincaré Type Inequalities

We establish the Poincaré-type inequalities for the composition of the homotopy operator, exterior derivative operator, and the projection operator withLφ-norm applied to the nonhomogeneousA-harmonic equation inLφ(Ω)-averaging domains.

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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