Entropy and renormalized solutions for a nonlinear elliptic problem in Musielak-Orlicz spaces
- Authors: Kozhevnikova L.M.1,2
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Affiliations:
- Sterlitamak Branch of Bashkir State University
- Elabuga Institute of Kazan Federal University
- Issue: Vol 69, No 1 (2023): Differential and Functional Differential Equations
- Pages: 98-115
- Section: Articles
- URL: https://journals.rudn.ru/CMFD/article/view/34596
- DOI: https://doi.org/10.22363/2413-3639-2023-69-1-98-115
- EDN: https://elibrary.ru/EBRPUC
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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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