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Absolute continuity of the best Sobolev constant of a bounded domain
Absolute continuity Lipschitz continuity p-Laplacian Rayleigh quotient Sobolev best constants
2012/6/7
Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N},...
Continuity of attractors for a nonlinear parabolic problem with terms concentrating in the boundary
Partial differential equations on infinite-dimensional spaces asymptotic behavior of solutions attractors singular perturbations concentrating terms
2012/4/17
We analyze the dynamics of the flow generated by a nonlinear parabolic problem when some reaction and potential terms are concentrated in a neighborhood of the boundary. We assume that this neighborho...
Holder continuity and injectivity of optimal maps
Holder continuity injectivity of optimal maps Analysis of PDEs Differential Geometry
2011/8/25
Abstract: Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c...
Hôlder continuity of solutions of second-order non-linear elliptic integro-differential equations
H¨older regularity integro-differential equations L´ evy operators general non-local operators
2010/11/29
This paper is concerned with H¨older regularity of viscosity solutions of second-order, fully
non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we ass...
H¨older continuity of the weak solutions for parabolic equations with the nonstandard growth condition
Boundedness H\
2007/12/12
In this paper, we investigate the interior regularity including the local boundedness and the interior H\"{o}lder continuity of weak solutions for parabolic equations of the $p(x,t)$-Laplacian type. W...