Equivalence of Entropy and Renormalized Solutions of a Nonlinear Elliptic Problem in Musielak–Orlicz Spaces

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 do...

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Bibliographic Details
Published in:Differential equations 2023, Vol.59 (1), p.34-50
Main Authors: Kozhevnikova, L. M., Kashnikova, A. P.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Differential equations
Dirichlet problem
Elliptic functions
Entropy
Equivalence
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Sobolev space
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Summary: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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266123010044