Regularity estimates for the oblique derivative problem on non-smooth domains. I
type: Item
instance of: scholarly article
title: Regularity estimates for the oblique derivative problem on non-smooth domains. I
zbMATH Open document ID: 0841.35018
author: Pengfei Guan
author: Eric T. Sawyer
published in: Chinese Annals of Mathematics. Series B
publication date: 1995-10-18T00:00:00Z
review text: The authors consider the existence and regularity of the oblique derivative problem \(Pu= f\) in \(\Omega\), \(\vec lu= g\) on \(\partial\Omega\), where \(P\) is a second-order elliptic differential operator on \(\mathbb{R}^n\), \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) and \(\vec l\) is a unit vector field on the boundary of \(\Omega\) (which may be tangential to the boundary). All above are assumed with limited smoothness. The authors show that the solution \(u\) has an elliptic gain from \(f\) in Hölder spaces and they obtain \(L^p\) regularity of \(u\) generalizing some results from \textit{P. F. Guan} and \textit{E. Sawyer} [Ann. Math., II. Ser. 137, 1-70 (1993; Zbl 0792.35039)] to the limited smooth case. Some applied nonlinear problems are also discussed.
reviewed by: Josef Danéček
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 807018
zbMATH Keywords: degenerate boundary value problem
zbMATH Keywords: limited smoothness
zbMATH Keywords: \(L^ p\) regularity
MaRDI profile type: Publication
Recommended article: Regularity estimates for the oblique derivative problem on non-smooth domains. II
Recommended article: Regularity estimates for the oblique derivative problem
Recommended article: Q5698860
Recommended article: On the regularity of the oblique derivative problem for quasilinear elliptic systems
Recommended article: Q3364610
Recommended article: Q3974273
Recommended article: On oblique derivative problems for fully nonlinear second-order elliptic partial differential equations on nonsmooth domains
Recommended article: Oblique derivative problems for the Laplacian in Lipschitz domains
Recommended article: Q3832929
Recommended article: Pointwise estimates for oblique derivative problems in nonsmooth domains
description: scientific article; zbMATH DE number 807018