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Abstract
We consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ 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 $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.
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- Copyright (2020 Juliusz Schauder Centre for Nonlinear Studies, Nicolaus Copernicus University in Toruń)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
Topological Methods in Nonlinear Analysis
no. 55,
pages 583 - 600,
ISSN: 1230-3429 - Language:
- English
- Publication year:
- 2020
- Bibliographic description:
- Maksymiuk J., Wroński K.: Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces// Topological Methods in Nonlinear Analysis -Vol. 55,iss. 2 (2020), s.583-600
- DOI:
- Digital Object Identifier (open in new tab) 10.12775/tmna.2019.106
- Verified by:
- Gdańsk University of Technology
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