Partial regularity for subquadratic parabolic systems with continuous coefficients
type: Item
instance of: scholarly article
title: Partial regularity for subquadratic parabolic systems with continuous coefficients
zbMATH Open document ID: 1252.35100
author: Joe Geisbauer
author: Mikil Foss
published in: Manuscripta Mathematica
publication date: 2012-09-19T00:00:00Z
review text: The authors consider singular parabolic quasilinear equations of the type \[ u_t =\operatorname{div }a(x,t, u, Du) \] where \(a\) is a vector field satisfying subquadratic growth and ellipticity conditions. They only require that the coefficients of the system are continuous with respect to the first two arguments. Under these assumptions, they are able to prove that there is an open subset with full measure of the solution's domain, on which the solution is Hölder continuous. A similar result was conjectured by Campanato several years ago. In the last years, this regularity problem was faced under different assumptions, especially in the elliptic case, by several researchers, among them we quote Baroni, Boegelein, Duzaar, Mingione and Steffen. In this paper, an essential tool is the DiBenedetto's intrinsing scaling approach. Moreover, we remark that the authors adapt the classical \(A\)-caloric approximation lemma to this specific case.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 35K67
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 6084031
zbMATH Keywords: intrinsic scaling approach
zbMATH Keywords: Campanato's conjecture
zbMATH Keywords: \(A\)-caloric approximation lemma
MaRDI profile type: Publication
full work available at URL: s00229-011-0502-5
OpenAlex ID: W2052288393
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DOI: 10.1007/S00229-011-0502-5
description: scientific article; zbMATH DE number 6084031