Renormalized solutions of elliptic equations with variable exponents and general measure data. (December 2020)

• Record Type: Journal Article
• Authors: Kozhevnikova, L. M.
• Is Part Of: Sbornik. Volume 211:Number 12(2020)
• Page Start: 1737
• Page End: 1776
• Publication Date: 2020-12
• Subjects: 35J62; 35J92; quasilinear elliptic equation -- renormalized solution -- Radon measure -- variable exponent -- Dirichlet problem; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM9371
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: A class of second-order elliptic equations with variable nonlinearity exponents and the right-hand side in the form of the general Radon measure with finite total variation is considered. The existence of a renormalized solution of the Dirichlet problem is proved as a consequence of stability with respect to the convergence of the right-hand side of the equation. Bibliography: 37 titles.