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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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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description 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.
doi_str_mv 10.1134/S0012266123010044
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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
title Equivalence of Entropy and Renormalized Solutions of a Nonlinear Elliptic Problem in Musielak–Orlicz Spaces
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