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

In this paper, we establish the equivalence of entropy and renormalized solutions of secondorder elliptic equations with nonlinearities defined by the Musielak–Orlicz functions and the right-hand side from the space L 1 (Ω) . In nonreflexive Musielak–Orlicz–Sobolev spaces, we prove the existence and...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 283; no. 2; pp. 255 - 271
Main Author Kozhevnikova, L. M.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2024
Springer Nature B.V
Subjects
Dirichlet problem
Elliptic functions
Entropy
Mathematics
Mathematics and Statistics
Nonlinearity
Sobolev space
existence and uniqueness of solutions
renormalized solution
entropy solution
Musielak–Orlicz–Sobolev space
second-order elliptic equation
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Summary:In this paper, we establish the equivalence of entropy and renormalized solutions of secondorder elliptic equations with nonlinearities defined by the Musielak–Orlicz functions and the right-hand side from the space L 1 (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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07253-3