On the Hölder property of one elliptic equation
type: Item
instance of: scholarly article
title: On the Hölder property of one elliptic equation
zbMATH Open document ID: 1137.35383
published in: Journal of Mathematical Sciences (New York)
publication date: 2006-01-23T00:00:00Z
review text: The paper deals with an elliptic in the unit disk equation of the divergence form with discontinuity lines coinciding with the two-dimensional coordinate system axes. On the above lines it has the order degeneration in the second and forth quadrants as a power function of the radius of the order \(\alpha\) and with the order \(-\alpha\), \(0<\alpha<2\), in the first and third quadrants. Introducing in the natural way classes of generalized solutions in the corresponding weighted Sobolev space, the Hölder property of the solutions of the equation under consideration is studied.
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5000619
zbMATH Keywords: degenerate elliptic equations
zbMATH Keywords: discontinuous coefficients
zbMATH Keywords: generalized solutions
zbMATH Keywords: Hölder property of solutions
zbMATH Keywords: weighted Sobolev spaces
author: Yu. A. Alkhutov
author: V. V. Zhikov
reviewed by: G. Jaiani
MaRDI profile type: Publication
full work available at URL: s10958-005-0290-0
OpenAlex ID: W2002776338
cites work: On the Hölder property of solutions of degenerate elliptic equations.
cites work: The local regularity of solutions of degenerate elliptic equations
cites work: Weighted Norm Inequalities for the Hardy Maximal Function
cites work: Weighted Sobolev spaces
cites work: To the problem of passage to the limit in divergent nonuniformly elliptic equations
DOI: 10.1007/S10958-005-0290-0
Recommended article: On the Hölder property of solutions of degenerate elliptic equations.
Recommended article: Q3218486
Recommended article: Q3803499
Recommended article: Hölder estimates for a class of degenerate elliptic equations
Recommended article: Q4017933
Recommended article: Hölder continuity of solutions of an elliptic equation uniformly degenerating on part of the domain
Recommended article: Hölder continuity of solutions of some degenerate elliptic differential equations
Recommended article: Hölder ratio of solutions of elliptic equations with a point on the boundary.
Recommended article: Q3633537
Recommended article: An alternative approach to the Hölder continuity of solutions to some elliptic equations
description: scientific article; zbMATH DE number 5000619