Hölder regularity for porous medium systems
type: Item
instance of: scholarly article
title: Hölder regularity for porous medium systems
zbMATH Open document ID: 1472.35078
author: Naian Liao
published in: Calculus of Variations and Partial Differential Equations
publication date: 2021-08-24T00:00:00Z
review text: In this paper, the author considers locally bounded weak solutions to certain parabolic systems of porous medium type, i.e. \[ \partial_t u-\mathrm{div}(m|u|^{m-1}Du) = 0, \] with \( m > 0\). As it is well known, everywhere regularity is in general not expected from systems of elliptic or parabolic type, nevertheless, the special quasi-diagonal structure of thus system, enables the author to achieve the Hölder regularity of locally bounded solutions. As a consequence of the local Hölder estimates, a Liouville type result for bounded global solutions is also established. In addition, sufficient conditions are given to ensure local boundedness of local weak solutions.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K67
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 7384537
zbMATH Keywords: parabolic systems of porous medium type
zbMATH Keywords: local Hölder regularity
zbMATH Keywords: Liouville estimates
zbMATH Keywords: local boundedness
zbMATH Keywords: quasi-diagonal structure
Wikidata QID: Q115386553
MaRDI profile type: Publication
full work available at URL: s00526-021-02021-6
OpenAlex ID: W3185335247
cites work: Regularity of weak solutions and supersolutions to the porous medium equation
cites work: Hölder continuity of the gradient of solutions of nonlinear degenerate parabolic systems
cites work: Hölder continuity of the gradient of the solutions of certain degenerate parabolic equations
cites work: Degenerate parabolic equations
cites work: C1 + α local regularity of weak solutions of degenerate elliptic equations
cites work: Harnack's Inequality for Degenerate and Singular Parabolic Equations
cites work: Hölder estimates for nonlinear degenerate parabolic sytems.
cites work: On the partial regularity of weak solutions on nonlinear parabolic systems
cites work: Local continuity and asymptotic behaviour of degenerate parabolic systems
cites work: Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation
cites work: Systems of partial differential equations in porous medium
cites work: Q5562267
cites work: Everywhere Regularity of Solutions to a Class of Strongly Coupled Degenerate Parabolic Systems
cites work: A unified approach to the Hölder regularity of solutions to degenerate and singular parabolic equations
cites work: Everywhere regularity of certain nonlinear diffusion systems
cites work: On the temporal decay estimates for the degenerate parabolic system
cites work: On \(C_{\alpha}\)-regularity of the gradient of solutions of degenerate parabolic systems
cites work: Global solutions to a class of strongly coupled parabolic systems
cites work: On a degenerate parabolic system
DOI: 10.1007/S00526-021-02021-6
description: scientific article; zbMATH DE number 7384537