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Existence of renormalized solutions to fully anisotropic and inhomogeneous elliptic problems

Part of: Elliptic equations and systems Representations of solutions

Published online by Cambridge University Press:  31 October 2023

Bartosz Budnarowski  and
Ying Li
Bartosz Budnarowski
Affiliation:
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw ul. Banacha 2, 02-097 Warsaw, Poland ([email protected])
Ying Li
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, China ([email protected])
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Abstract

We will present the proof of existence and uniqueness of renormalized solutions to a broad family of strongly non-linear elliptic equations with lower order terms and data of low integrability. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak–Orlicz spaces. The setting considered in this paper generalized known results in the variable exponents, anisotropic polynomial, double phase and classical Orlicz setting.

Keywords

existenceelliptic boundary value problemsrenormalized solutionsMusielak–Orlicz spaces

MSC classification

Primary: 35D30: Weak solutions
Secondary: 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 37
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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