On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent [PDF]
, 2006 We consider the nonlinear eigenvalue problem $-{\rm div}(|\nabla u|^{p(x)-2}\nabla u)=\lambda |u|^{q(x)-2}u$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded open set in $\RR^N$ with smooth boundary and $p$, $q$ are continuous ...
Mihailescu, Mihai, Radulescu, Vicentiu
core +1 more source
On the Dirichlet Problem Generated by the Maz'ya--Sobolev Inequality [PDF]
arXiv, 2011 We discuss the attainability of sharp constants for the Maz'ya--Sobolev inequalities in wedges, "perturbed" wedges and bounded domains.
arxiv
Absolute continuity of the best Sobolev constant of a bounded domain
, 2012 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 ...
Antonietti +10 more
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Regularity for variational problems in the Heisenberg group [PDF]
arXiv, 2017 We study the regularity of minima of scalar variational integrals of $p$-growth, $1
arxiv
Besov regularity for the elliptic p-harmonic equations in the non-quadratic case
Advances in Nonlinear AnalysisIn this article, we mainly establish the local extra fractional differentiability (Besov regularity) of weak solutions for the following divergence nonlinear elliptic equations of pp-Laplacian type: divA(Du,x)=divF,\hspace{0.1em}\text{div}\hspace{0.1em}A(
Yao Fengping
doaj +1 more source
A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type [PDF]
arXiv, 2003 We establish Holder continuity of weak solutions to degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type.
arxiv
Global and blow up solutions to cross diffusion systems
Advances in Nonlinear Analysis, 2015 Necessary and sufficient conditions for global existence of classical solutions to a class of cross diffusion systems on n-dimensional domains are given. Examples of blow up solutions are also presented.
Ahmad Shair, Le Dung
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On Removable Singularities of Solutions of Higher-Order Differential Inequalities
Advanced Nonlinear Studies, 2020 We obtain sufficient conditions for solutions of the mth-order differential ...
Kon’kov A. A., Shishkov A. E.
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First eigenvalue and Maximum principle for fully nonlinear singular operators [PDF]
arXiv, 2004 Through the Maximum principle we define the principal eigenvalue for a class of fully-nonlinear operators that are the non-variational equivalent of the p-Laplacian. We also obtain some a priori Holder estimates for non-negative solutions below that eigenvalue.
arxiv
On the fundamental eigenvalue ratio of the p-Laplacian [PDF]
arXiv, 2004 It is shown that the fundamental eigenvalue ratio \lambda_2 / \lambda_1 of the p-Laplacian is bounded by a quantity depending only on the dimension N and p.
arxiv