Nonlinear potential theory and PDEs
type: Item
instance of: scholarly article
title: Nonlinear potential theory and PDEs
zbMATH Open document ID: 0844.35027
DOI: 10.1007/BF01047838
author: Tero Kilpeläinen
published in: Potential Analysis
publication date: 1994-04-19T00:00:00Z
review text: The author considers a class of equations similar to \((*)\) \(-\text{div}(|\nabla u|^{p- 2} \nabla u)= \mu\), where \(\mu\) is a nonnegative Radon measure and \(1< p< \infty\). The main topics discussed are the relation between \(p\)-superharmonic functions and distributional solutions of \((*)\), and the Wiener criterion for the regularity of boundary points for such equations.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 31C15
zbMATH DE Number: 554334
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: \({\mathcal A}\)-superharmonic functions
zbMATH Keywords: Wiener's criterion
zbMATH Keywords: regularity of boundary points
reviewed by: John Urbas
MaRDI profile type: Publication
cites work: Nonlinear elliptic and parabolic equations involving measure data
cites work: A regularity condition at the boundary for solutions of quasilinear elliptic equations
cites work: Conformally Invariant Variational Integrals
cites work: Thin sets in nonlinear potential theory
cites work: A-superharmonic functions and supersolutions of degenerate elliptic equations
cites work: Fine topology and quasilinear elliptic equations
cites work: Q4693180
cites work: Weak minima of variational integrals.
cites work: Q4033095
cites work: On the definition and properties of p-superharmonic functions.
cites work: Two theorems of N. Wiener for solutions of quasilinear elliptic equations
cites work: Quasilinear elliptic problems with measures as data
cites work: Local Behavior of Solutions of Quasilinear Elliptic Equations With General Structure
cites work: Q5518040
full work available at URL: https://doi.org/10.1007/bf01047838
OpenAlex ID: W4233159266
description: scientific article; zbMATH DE number 554334