Regularity of the solution of the Cauchy problem for a higher-order parabolic equation
type: Item
instance of: scholarly article
title: Regularity of the solution of the Cauchy problem for a higher-order parabolic equation
zbMATH Open document ID: 1213.35245
DOI: 10.1134/S0012266110040105
author: M. F. Cherepova
published in: Differential Equations
publication date: 2010-12-08T00:00:00Z
review text: This paper is concerned with the regularity of solutions to some Cauchy problems of parabolic type of order \(2m\). The author obtains the solvability of such problems in the class of weighted Hölder space of order \(2m\) by combining the method of potentials and the method of continuation with respect to a parameter. The only assumption required in the paper is that the right-hand side and lower order coefficients of the equation satisfy a certain growth condition when approaching the plane that is the support of the initial data while the higher order are not required to satisfy the Dini condition near the support plane.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 35K30
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5824105
zbMATH Keywords: higher-order parabolic problem
zbMATH Keywords: Cauchy problem
zbMATH Keywords: regularity
zbMATH Keywords: Hölder class
zbMATH Keywords: weighted Hölder space
zbMATH Keywords: Dini condition near the support plane
Wikidata QID: Q115252550
MaRDI profile type: Publication
cites work: Q5548527
cites work: On the solvability of boundary value problems for a parabolic equation with coefficients growing near the boundary
cites work: Q4252673
full work available at URL: s0012266110040105
OpenAlex ID: W2064330887
description: scientific article; zbMATH DE number 5824105