\(C^{1,\alpha}\) regularity of interface of some nonlinear degenerate parabolic equations
type: Item
instance of: scholarly article
title: \(C^{1,\alpha}\) regularity of interface of some nonlinear degenerate parabolic equations
zbMATH Open document ID: 0961.35076
DOI: 10.1016/S0362-546X(99)00127-3
author: Youngsang Ko
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-05-15T00:00:00Z
review text: The author considers the equation \(u_t=\text{div} (|\nabla u^m|)^{p-2} \nabla u^m\) in \({\mathbb R}^N \times (0,T)\) with the initial condition \(u(x,0) =u_0 (x)\). It is known that there is an interface that separates the region where \(u>0\) from the region where \(u=0\). Let \(\Omega \) be a region where \(u>0\), \(\Gamma = \partial \Omega \cap {t>0}\). The main result is concluded in the regularity of \(\Gamma \). Namely the author establishes under natural assumptions that \(\Gamma\) is presented by a \(C^{1, \alpha }\) function, i.e. a Lipschitz continuous function.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1529442
zbMATH Keywords: degenerate equation
zbMATH Keywords: regularity of interface
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
cites work: Q3786839
cites work: C1,α regularity of the free boundary for the n-dimensional porous media equation
cites work: Hölder continuity of the gradient of the solutions of certain degenerate parabolic equations
cites work: Regularity for the Interfaces of Evolutionary <scp>p</scp>-Laplacian Functions
cites work: Degenerate parabolic equations
cites work: Q3490360
cites work: Hölder estimates for quasilinear doubly degenerate parabolic equations
cites work: Q5562267
cites work: On \(C_{\alpha}\)-regularity of the gradient of solutions of degenerate parabolic systems
cites work: Lipschitz continuity of the free boundary of some nonlinear degenerate parabolic equations
Wikidata QID: Q126340427
full work available at URL: s0362-546x(99)00127-3
OpenAlex ID: W2058332430
description: scientific article; zbMATH DE number 1529442