Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces. (1st April 2022)

• Record Type: Journal Article
• Authors: Kashnikova, A. P.; Kozhevnikova, L. M.
• Is Part Of: Sbornik. Volume 213:Number 4(2022)
• Page Start: 476
• Page End: 511
• Publication Date: 2022-04-01
• Subjects: 35J62; 35J15; quasilinear elliptic equation -- entropy solution -- renormalized solution -- unbounded domain -- diffuse measure -- Musielak-Orlicz space; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM9632
• Languages: English
• ISSNs: 1064-5616

Abstract

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.