Hölder continuity for Trudinger's equation in measure spaces
type: Item
instance of: scholarly article
title: Hölder continuity for Trudinger's equation in measure spaces
zbMATH Open document ID: 1252.35101
author: Tuomo Kuusi
author: Rojbin Laleoglu
author: Juhana Siljander
author: José Miguel Urbano
published in: Calculus of Variations and Partial Differential Equations
publication date: 2012-09-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1103.1845
review text: The authors consider the so-called Trudinger equations, i.e., quasilinear parabolic equations of the type \[ u^{p-1}_t = \nabla ( |\nabla u |^{p-2}\nabla u). \] They study the singular case (i.e., the case \(1<p<2\)). The authors already proved the Hölder regularity of the solutions for such kind of equations for the degenerate case in the setting of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. In this paper, the authors extend this result to the singular case. In the proof, the authors use some recent Harnack estimates and an intrinsic scaling approach.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K92
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35K67
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 6087752
zbMATH Keywords: intrinsic scaling method
zbMATH Keywords: Harnack estimates
MaRDI profile type: Publication
OpenAlex ID: W1975228793
Wikidata QID: Q115387511
arXiv ID: 1103.1845
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DOI: 10.1007/S00526-011-0456-1
description: scientific article; zbMATH DE number 6087752