Solutions of singular elliptic equations via the oblique derivative problem
type: Item
instance of: scholarly article
title: Solutions of singular elliptic equations via the oblique derivative problem
zbMATH Open document ID: 1225.35107
author: Gary M. Lieberman
published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche
publication date: 2011-09-13T00:00:00Z
review text: The author studies a class of second order elliptic equations whose highest order coefficients vanish everywhere on the boundary. Under suitable conditions on the lower order coefficients, \textit{M. Langlais} [Proc. Lond. Math. Soc., III. Ser. 50, 282--298 (1985; Zbl 0566.35052)] proved that such equations have unique smooth solutions up to the boundary provided the data are smooth enough. The author proves some Schauder estimates for these equations even in Lipschitz domains. In addition, the author shows that bounded solutions of such problems are as smooth as the data allow. A key step to get these new results consists in noting that smooth solutions must satisfy an oblique derivative boundary condition and in applying the techniques developed by the author to study the oblique derivative problem in the case of non-degenerate elliptic equations.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35J75
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35J67
zbMATH DE Number: 5947316
zbMATH Keywords: singular elliptic equations
zbMATH Keywords: oblique derivative problem
zbMATH Keywords: a priori estimates
zbMATH Keywords: smoothness of solutions
MaRDI profile type: Publication
full work available at URL: s11565-010-0113-1
OpenAlex ID: W2001087638
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DOI: 10.1007/S11565-010-0113-1
description: scientific article; zbMATH DE number 5947316