Hölder continuity of solutions to quasilinear elliptic equations involving measures
type: Item
instance of: scholarly article
title: Hölder continuity of solutions to quasilinear elliptic equations involving measures
zbMATH Open document ID: 0813.35016
DOI: 10.1007/BF01468246
author: Tero Kilpeläinen
published in: Potential Analysis
publication date: 1994-10-09T00:00:00Z
review text: This article contains sharp regularity results for solutions of nonhomogeneous quasilinear elliptic equations whose prototype is \[ -\text{div} \bigl( | \nabla u |^{p-2} \nabla u \bigr) = \mu, \] where \(\mu\) is a positive measure satisfying the condition \(\mu \bigl( B(x,r) \bigr)\leq Mr^ \rho\). It turns out that the solution \(u\) is Hölder continuous if and only if \(\rho > n - p\). The author proves that to get Hölder continuity of order \(\alpha\) it is enough to have \(\rho > n - p + \alpha (p-1)\), and that this result is sharp in the sense that there are examples of solutions which are not Hölder continuous with exponent \(\beta\) if \(\rho < n - p+ \beta (p-1)\). Extensions of these results to the variable coefficient case are also presented.
reviewed by: Juan J. Manfredi
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 650841
zbMATH Keywords: sharp regularity results
zbMATH Keywords: quasilinear elliptic equations
zbMATH Keywords: Hölder continuity
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 650841