How to remember the Sobolev inequalities

1982 ◽  
pp. 97-109 ◽  
Author(s):  
Daniel B. Henry
Keyword(s):  
Sobolev Inequalities

scholarly journals Sobolev inequalities with jointly concave weights on convex cones

2020 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Cristian E. Gutiérrez ◽  
Alexandru Kristály
Keyword(s):  
Convex Cones ◽  
Sobolev Inequalities

scholarly journals Sobolev Inequalities for Functions on Graphs

2021 ◽  
Vol 1804 (1) ◽  
pp. 012132
Author(s):  
Eman Samir Bhaya ◽  
Zainab Flaih
Keyword(s):  
Sobolev Inequalities

scholarly journals Two types of discrete Sobolev inequalities on a weighted Toeplitz graph

2016 ◽  
Vol 507 ◽  
pp. 344-355 ◽  
Author(s):  
Kazuo Takemura ◽  
Atsushi Nagai ◽  
Yoshinori Kametaka
Keyword(s):  
Sobolev Inequalities

scholarly journals Sharp Sobolev inequalities for vector valued maps

2006 ◽  
Vol 253 (4) ◽  
pp. 681-708 ◽  
Author(s):  
Emmanuel Hebey
Keyword(s):  
Sobolev Inequalities ◽  
Vector Valued

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.

scholarly journals Lp-Lq estimates off the line of duality

1995 ◽  
Vol 58 (2) ◽  
pp. 154-166 ◽  
Author(s):  
J.-G. Bak ◽  
D. McMichael ◽  
D. Oberlin
Keyword(s):  
Sobolev Inequalities ◽  
Riesz Means ◽  
Negative Order

AbstractTheorems 1 and 2 are known results concerning Lp–Lq estimates for certain operators wherein the point (1/p, 1/q) lies on the line of duality 1/p + 1/q = 1. In Theorems 1′ and 2′ we show that with mild additional hypotheses it is possible to prove Lp-Lq estimates for indices (1/p, 1/q) off the line of duality. Applications to Bochner-Riesz means of negative order and uniform Sobolev inequalities are given.

Gauged Sobolev inequalities

2007 ◽  
Vol 86 (3) ◽  
pp. 367-402 ◽  
Author(s):  
Umberto Mosco
Keyword(s):  
Sobolev Inequalities
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