Developments and perspectives in Nonlinear Potential Theory. (May 2020)

• Record Type: Journal Article
• Authors: Mingione, Giuseppe; Palatucci, Giampiero
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: primary 35J60 -- secondary 31C45; Calderón–Zygmund theory -- Elliptic equations -- Nonlinear Potential Theory -- Regularity; 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.2019.02.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Nonlinear Potential theory aims at replicating the classical linear potential theory when nonlinear equations are considered. In recent years there has been a substantial development of this subject, mostly linked to the possibility of proving pointwise estimates for solutions to nonlinear equations via linear and nonlinear potentials. Here we give a brief account of such developments and outline the connections with different fields.