A Harnack's inequality for mixed type evolution equations
type: Item
instance of: scholarly article
title: A Harnack's inequality for mixed type evolution equations
zbMATH Open document ID: 1401.35008
author: Fabio Paronetto
published in: Journal of Differential Equations
publication date: 2016-01-26T00:00:00Z
review text: The author considers a class of evolution equations whose simplest example is \[ \mu(x) \frac{\partial u}{\partial t} = \Delta u \] where \(\mu\) can be positive, null and negative, so in particular elliptic-parabolic and forward-backward parabolic equations are included. By using suitable homogeneous parabolic De Giorgi classes of order 2, the author proves local boundedness and shows a Harnack inequality which, as by-products, gives a maximum principle and Hölder-continuity, in particular along the interface where \(\mu\) changes sign.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J62
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 6535789
zbMATH Keywords: elliptic-parabolic equations
zbMATH Keywords: forward-backward parabolic equations
zbMATH Keywords: mixed type equations
zbMATH Keywords: weighted Sobolev spaces
zbMATH Keywords: Harnack's inequality
zbMATH Keywords: Hölder-continuity
MaRDI profile type: Publication
full work available at URL: j.jde.2015.12.003
OpenAlex ID: W2963312029
cites work: Hölder continuity of solutions to parabolic equations uniformly degenerating on a part of the domain
cites work: Sur une équation d'évolution changeant de type
cites work: On an equation of mixed type from electron scattering theory
cites work: Weighted Poincare and Sobolev Inequalities and Estimates for Weighted Peano Maximal Functions
cites work: Degenerate parabolic equations and Harnack inequality
cites work: A Harnack inequality for degenerate parabolic equations
cites work: A remark on a Harnack inequality for dengerate parabolic equations
cites work: Q3475640
cites work: Harnack estimates for quasi-linear degenerate parabolic differential equations
cites work: Harnack inequalities for quasi-minima of variational integrals
cites work: The local regularity of solutions of degenerate elliptic equations
cites work: Mean value and Harnack inequalities for a certain class of degenerate parabolic equations
cites work: Q3700300
cites work: Parabolic De Giorgi classes of order \(p\) and the Harnack inequality
cites work: Q3139888
cites work: Quasi-minima
cites work: Q3151387
cites work: Harnack's Inequality for Degenerate Parabolic Equations
cites work: Sobolev Interpolation Inequalities with Weights
cites work: On the behavior of the solutions of degenerate parabolic equations
cites work: Harnack's inequality for solutions of some degenerate elliptic equations.
cites work: On a forward-backward parabolic equation
cites work: A Harnack's inequality and Hölder continuity for solutions of mixed type evolution equations
cites work: Existence results for a class of evolution equations of mixed type
cites work: Q4469411
cites work: Q3104356
cites work: Degenerate parabolic initial-boundary value problems
cites work: A Harnack inequality for weighted degenerate parabolic equations
cites work: On the regularity of generalized solutions of linear, non-uniformly elliptic equations
cites work: Q4765475
cites work: Parabolic Q-minima and minimal solutions to variational flow
DOI: 10.1016/J.JDE.2015.12.003
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description: scientific article; zbMATH DE number 6535789