Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces

Abstract A second-order quasilinear elliptic equation with a measure of special form on the right-hand side is considered. Restrictions on the structure of the equation are imposed in terms of a generalized -function such that the conjugate function obeys the -condition and the corresponding Musiela...

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Bibliographic Details
Published inSbornik. Mathematics Vol. 213; no. 4; pp. 476 - 511
Main Authors Kashnikova, A. P., Kozhevnikova, L. M.
Format Journal Article
LanguageEnglish
Published Providence London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences 01.04.2022
IOP Publishing
Subjects
diffuse measure
Dirichlet problem
Elliptic functions
Entropy of solution
entropy solution
Musielak-Orlicz space
Orlicz space
quasilinear elliptic equation
renormalized solution
unbounded domain
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Summary:Abstract A second-order quasilinear elliptic equation with a measure of special form on the right-hand side is considered. Restrictions on the structure of the equation are imposed in terms of a generalized -function such that the conjugate function obeys the -condition and the corresponding Musielak-Orlicz space is not necessarily reflexive. In an arbitrary domain satisfying the segment property, the existence of an entropy solution of the Dirichlet problem is proved. It is established that this solution is renormalized. Bibliography: 29 titles.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9632