Summability of solutions of the Dirichlet problem for nonlinear elliptic equations with right-hand side in logarithmic classes close to L1. (March 2020)

• Record Type: Journal Article
• Authors: Kovalevsky, Alexander A.
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 35B65 -- 35J25 -- 35J60; Nonlinear elliptic equations -- Dirichlet problem -- Weak solution -- Entropy solution -- Summability of solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111692
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the Dirichlet problem for a class of nonlinear elliptic second-order equations with right-hand side in L 1 . We describe the summability properties of entropy and weak solutions of this problem in the case where the right-hand side belongs to classes close to L 1 and defined by the logarithmic function or its compositions of arbitrary multiplicity.