Email this article Equivalence of Entropy and Renormalized Solutions of a Nonlinear Elliptic Problem in Musielak–Orlicz Spaces
- Authors: Kozhevnikova L.M1,2, Kashnikova A.P1
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Affiliations:
- Sterlitamak Branch of Bashkir University of Science and Technology, Sterlitamak, Bashkortostan, 453103, Russia
- Elabuga Institute of Kazan Federal University, Elabuga, Tatarstan, 423600, Russia
- Issue: Vol 59, No 1 (2023)
- Pages: 35-50
- Section: Articles
- URL: https://journals.rcsi.science/0374-0641/article/view/144899
- DOI: https://doi.org/10.31857/S0374064123010053
- EDN: https://elibrary.ru/OBVGXN
- ID: 144899
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Abstract
We consider second-order elliptic equations with nonlinearities determined by Musielak–Orlicz functions and with right-hand side in the space. In the Musielak–Orlicz–Sobolev spaces, we establish some properties and uniqueness of both entropy and renormalized solutions of the Dirichlet problem in domains with Lipschitz boundary. In addition, the equivalence and sign-definiteness of the entropy and renormalized solutions is proved.
About the authors
L. M Kozhevnikova
Sterlitamak Branch of Bashkir University of Science and Technology, Sterlitamak, Bashkortostan, 453103, Russia; Elabuga Institute of Kazan Federal University, Elabuga, Tatarstan, 423600, Russia
Email: kosul@mail.ru
A. P Kashnikova
Sterlitamak Branch of Bashkir University of Science and Technology, Sterlitamak, Bashkortostan, 453103, Russia
Author for correspondence.
Email: a.kashnikova98@yandex.ru
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