Nonlinear Potential Theory of elliptic systems. (June 2016)

• Record Type: Journal Article
• Authors: Kuusi, Tuomo; Mingione, Giuseppe
• Is Part Of: Nonlinear analysis. Volume 138(2016)
• Page Start: 277
• Page End: 299
• Publication Date: 2016-06
• Subjects: Nonlinear Potential Theory -- Regularity -- Elliptic equations; 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.2015.12.022
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We give a summary of recent results from Nonlinear Potential Theory, focusing on linear and nonlinear potential estimates of solutions to non-homogeneous equations and systems. We start with the cases of quasilinear, possibly degenerate equations of p -Laplacian type, and, passing through fully nonlinear elliptic equations, finally move to systems. In this last case we describe recent results implying potential estimates for the p -Laplacian system. Finally, we describe results bridging Nonlinear Potential Theory and classical partial regularity theory for general elliptic systems. The main outcomes are new ε -regularity criteria involving both excess functionals and nonlinear potentials.