Entropy and renormalized solutions for a nonlinear elliptic problem in Musielak-Orlicz spaces

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Abstract

In this paper, we establish the equivalence of entropy and renormalized solutions of second-order elliptic equations with nonlinearities defined by the Musielak-Orlicz functions and the right-hand side from the space L1(Ω). In nonreflexive Musielak-Orlicz-Sobolev spaces, we prove the existence and uniqueness of both entropy and renormalized solutions of the Dirichlet problem in domains with a Lipschitz boundary.

About the authors

L. M. Kozhevnikova

Sterlitamak Branch of Bashkir State University; Elabuga Institute of Kazan Federal University

Author for correspondence.
Email: kosul@mail.ru
Sterlitamak, Russia; Elabuga, Russia

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Copyright (c) 2023 Kozhevnikova L.M.

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