Mixed boundary value problems for elliptic and parabolic differential equations of second order
type: Item
instance of: scholarly article
title: Mixed boundary value problems for elliptic and parabolic differential equations of second order
zbMATH Open document ID: 0609.35021
DOI: 10.1016/0022-247X(86)90314-8
author: Gary M. Lieberman
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The author considers mixed boundary value problems either for elliptic or parabolic linear differential operators of second order. He is concerned with the existence, uniqueness and regularity of the solutions in fairly general circumstances. For instance, say that B is a first order oblique differential operator on a relatively open subset S of the boundary \(\partial \Omega\) of \(\Omega\) (a bounded connected open subset of \({\mathbb{R}}^ n)\) and consider the problem \[ Lu=f\quad in\quad \Omega;\quad Bu=g\quad on\quad S;\quad u=h\quad on\quad \partial \Omega \setminus S. \] The author's results include the case where \(\bar S\) and \(\partial \Omega \setminus S\) meet at arbitrary angles provided that \(\partial \Omega \setminus S\) is Lipschitz. The author proves the above result by using techniques of super and subsolutions (known as Perron's method) with appropriate adaptations due to the same author [Adv. Math. 55, 161-172 (1985; Zbl 0567.35037)].
Mathematics Subject Classification ID: 35G15
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 3985741
zbMATH Keywords: mixed boundary value problems
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: regularity
zbMATH Keywords: first order oblique differential operator
zbMATH Keywords: super and subsolutions
zbMATH Keywords: Perron's method
reviewed by: G. Perla Menzala
MaRDI profile type: Publication
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full work available at URL: 0022-247x(86)90314-8
OpenAlex ID: W1976976173
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description: scientific article; zbMATH DE number 3985741