On the existence of generalized solutions with finite Dirichlet integral for basic exterior boundary value problems
type: Item
instance of: scholarly article
title: On the existence of generalized solutions with finite Dirichlet integral for basic exterior boundary value problems
zbMATH Open document ID: 0737.35019
author: R. I. Simeonov
published in: Moscow University Mathematics Bulletin
publication date: 1992-06-25T00:00:00Z
review text: The author considers the Dirichlet and Neumann problems for the elliptic equation \[ (a^{ij}(z)u_{z_ j})_{z_ i}=f(z), z\in\Omega', \] where \(z=(x,y),\;\Omega'=\omega\times\mathbb{R}^ k\) and \(\omega\subset\mathbb{R}^ n\) is a domain with bounded complement. It is assumed that \(a^{ij}\) and \(f\) are 1-periodic with respect to the components of \(y\in\mathbb{R}^ k\). The finiteness of the Dirichlet integral of a solution is examined.
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 10658
zbMATH Keywords: exterior boundary value problems
zbMATH Keywords: Dirichlet and Neumann problems
zbMATH Keywords: Dirichlet integral
reviewed by: G. Vainikko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 10658