Existence of Solutions for Some Nonlinear Elliptic Equations in Musielak Spaces with Only the Log-Hölder Continuity Condition

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.

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

Kozhevnikova

Kashnikova²

2023

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Existence of Solutions for Some Nonlinear Elliptic Equations in Musielak Spaces with Only the Log-Hölder Continuity Condition

Cited by 7 publications

References 13 publications

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

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

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

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

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