A priori bounds for degenerate and singular evolutionary partial integro-differential equations
type: Item
instance of: scholarly article
title: A priori bounds for degenerate and singular evolutionary partial integro-differential equations
zbMATH Open document ID: 1205.45011
author: Vicente Vergara
author: Rico Zacher
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-10-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.1883
full work available at URL: http://hdl.handle.net/10533/144953
review text: The authors study quasilinear evolutionary partial integro-differential equations of second order which include time fractional \(p\)-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique [cf. e.g. \textit{E. Di Benedetto}, Degenerate parabolic equations, New York, NY: Springer-Verlag (1993; Zbl 0794.35090)] they establish results asserting the global boundedness of appropriately defined weak solutions of these problems. It is also showed that a maximum principle is valid for such equations. The authors further prove that in the case of so-called homogeneous structures the weak maximum principle for weak solutions takes the same form as in the classical parabolic case.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 35K92
zbMATH DE Number: 5800129
zbMATH Keywords: integro-differential equation
zbMATH Keywords: quasilinear equation
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: fractional derivative
zbMATH Keywords: degenerate parabolic equation
zbMATH Keywords: weak solution
zbMATH Keywords: energy estimates
zbMATH Keywords: De Giorgi technique
MaRDI profile type: Publication
OpenAlex ID: W2158950548
arXiv ID: 1007.1883
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DOI: 10.1016/J.NA.2010.07.039
description: scientific article