The Perron process applied to oblique derivative problems
type: Item
instance of: scholarly article
title: The Perron process applied to oblique derivative problems
zbMATH Open document ID: 0567.35027
DOI: 10.1016/0001-8708(85)90019-2
author: Gary M. Lieberman
published in: Advances in Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The author gives another proof of the solvability of the regular oblique derivative problem for a linear elliptic equation in Hölder spaces. The slight difference to chapter 6.7 of the well known monograph of \textit{D. Gilbarg} and \textit{N. S. Trudinger} [Elliptic partial differential equations of second order (1977; Zbl 0361.35003)] consists of the fact, that by using the same a-priori-estimates and a continuity method first a suitable defined local solvability is proved and second a solution is obtained by a Perron-process from local subsolution. - To my opinion in contrast to the claim this method does not seem to be more elementary than the treatment in the monograph cited above.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3905071
zbMATH Keywords: solvability
zbMATH Keywords: regular oblique derivative problem
zbMATH Keywords: Hölder spaces
zbMATH Keywords: a- priori-estimates
zbMATH Keywords: continuity method
zbMATH Keywords: Perron-process
reviewed by: Michael Wiegner
MaRDI profile type: Publication
full work available at URL: 0001-8708(85)90019-2
OpenAlex ID: W2036780843
cites work: Intermediate Schauder estimates
cites work: Q4040640
cites work: Q5549292
cites work: Q5581926
cites work: Mixed boundary value problems for elliptic and parabolic differential equations of second order
cites work: A general theory for linear elliptic partial differential equations
cites work: Sul problema misto per le equazioni lineari ellittiche
description: scientific article; zbMATH DE number 3905071