Geodesic
Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces
Sbornik. Mathematics, Tome 213 (2022) no. 4, pp. 476-511

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $N$-function such that the conjugate function obeys the $\Delta_2$-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.
Keywords: quasilinear elliptic equation, entropy solution, renormalized solution, unbounded domain, diffuse measure, Musielak-Orlicz space. 
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     author = {A. P. Kashnikova and L. M. Kozhevnikova},
     title = {Existence of solutions of nonlinear elliptic equations with measure data in {Musielak-Orlicz} spaces},
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A. P. Kashnikova; L. M. Kozhevnikova. Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces. Sbornik. Mathematics, Tome 213 (2022) no. 4, pp. 476-511. http://geodesic.mathdoc.fr/item/SM_2022_213_4_a2/