The Dirichlet problem for a second-order elliptic equation with an \(L_{p}\) boundary function
type: Item
instance of: scholarly article
zbMATH Open document ID: 1244.35038
author: A. K. Gushchin
published in: Sbornik: Mathematics
publication date: 2012-05-30T00:00:00Z
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 6039339
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: boundary values in Lebesgue spaces with \(p >1\)
zbMATH Keywords: second-order elliptic equation
MaRDI profile type: Publication
full work available at URL: sm2012v203n01abeh004211
OpenAlex ID: W1989421573
DOI: 10.1070/SM2012V203N01ABEH004211
title: The Dirichlet problem for a second-order elliptic equation with an \(L_{p}\) boundary function
review text: The main result of this paper is a unique solvability theorem for a Dirichlet problem where the boundary value lies in the Lebesgue spaces with \(p >1\), in a bounded domain in \(\mathbb R^n\). The weighted Sobolev spaces are involved, the weight being the distance from the boundary. The inward pointing normal on the boundary is assumed to be Dini continuous; the same property is also assumed for the equation coefficients, on the domain boundary. A very interesting example is given in the last part, concerning the possibility of a weaker condition for the uniqueness of the solution.
reviewed by: Gelu Paşa
description: scientific article; zbMATH DE number 6039339