Developments and perspectives in Nonlinear Potential Theory

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...

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Bibliographic Details
Published inNonlinear analysis Vol. 194; p. 111452
Main Authors Mingione, Giuseppe, Palatucci, Giampiero
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.05.2020
Elsevier BV
Subjects
Calderón–Zygmund theory
Elliptic equations
Mathematical analysis
Nonlinear equations
Nonlinear Potential Theory
Potential theory
Regularity
Replicating
secondary 31C45
primary 35J60
Regularity
Calderón–Zygmund theory
Elliptic equations
Nonlinear Potential Theory
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Summary: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.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2019.02.006