An extremum theory of the residual functional in Sobolev spaces \(W^{m,p}({\Omega{}})\)
type: Item
instance of: scholarly article
title: An extremum theory of the residual functional in Sobolev spaces \(W^{m,p}({\Omega{}})\)
zbMATH Open document ID: 0767.46030
DOI: 10.1007/BF02457373
author: Yongyong Ling
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1993-01-17T00:00:00Z
review text: Consider a properly posed problem of the partial differential equation \(L(u)=f\) and of the boundary value \(B(u)=g\) in the Sobolev space, where \(L\) and \(B\) are quasilinear and linear differential operators, respectively. In the paper under review a minimum existence theorem in the Sobolev space for the residual functional \[ J(u):=\| L(u)- f\|_ p^ p+\| B(u)-g\|_ p^ p \] is treated. Also, the weak compactness, force condition, lower semi-continuity and convexity of the residual functional are proved.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 96725
zbMATH Keywords: properly posed problem
zbMATH Keywords: partial differential equation
zbMATH Keywords: boundary value
zbMATH Keywords: Sobolev space
zbMATH Keywords: quasilinear
zbMATH Keywords: linear differential operators
zbMATH Keywords: minimum existence theorem
zbMATH Keywords: residual functional
zbMATH Keywords: weak compactness
zbMATH Keywords: force condition
zbMATH Keywords: lower semi-continuity
zbMATH Keywords: convexity
reviewed by: Rimas Norvaiša
MaRDI profile type: Publication
cites work: Analytic Inequalities
full work available at URL: https://doi.org/10.1007/bf02457373
OpenAlex ID: W2953625234
description: scientific article; zbMATH DE number 96725