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2020 Regularity of weak solutions for a class of elliptic PDEs in Orlicz-Sobolev spaces
Jakub Maksymiuk, Karol Wroński
Topol. Methods Nonlinear Anal. 55(2): 583-600 (2020). DOI: 10.12775/TMNA.2019.106

Abstract

We consider the elliptic partial differential equation in the divergence form \[ -{\rm div}(\nabla G(\nabla u(x)))+ F_u(x,u(x))=0, \] where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions. We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{\rm loc}\cap W^{1,\infty}_{\rm loc}$.

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Jakub Maksymiuk. Karol Wroński. "Regularity of weak solutions for a class of elliptic PDEs in Orlicz-Sobolev spaces." Topol. Methods Nonlinear Anal. 55 (2) 583 - 600, 2020. https://doi.org/10.12775/TMNA.2019.106

Information

Published: 2020
First available in Project Euclid: 11 June 2020

zbMATH: 07243987
MathSciNet: MR4131168
Digital Object Identifier: 10.12775/TMNA.2019.106

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.55 • No. 2 • 2020
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