Shape optimization for semi-linear elliptic equations based on an embedding domain method
type: Item
instance of: scholarly article
title: Shape optimization for semi-linear elliptic equations based on an embedding domain method
zbMATH Open document ID: 1077.49031
published in: Applied Mathematics and Optimization
publication date: 2004-09-22T00:00:00Z
review text: The author studies shape optimization problems for semilinear elliptic equations with homogeneous Dirichlet boundary conditions in two dimension. A part of the boundary of the domain is parametrized by a smooth function \(\gamma\) from \([0,1]\) into \textbf{R}. Using the method of fictitious domains the author proves the continuity of the solution to the state equation with respect to variations of the domain, i.e., with respect to \(\gamma\). Next the Fréchet differentiability of a quadratic cost functional with respect to variations of the domain is also studied.
reviewed by: J-P Raymond
Mathematics Subject Classification ID: 49Q10
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 65N99
zbMATH DE Number: 2101891
zbMATH Keywords: domain optimization
zbMATH Keywords: semilinear elliptic equations
zbMATH Keywords: embedding domain technique
zbMATH Keywords: fictitious domain method
author: Thomas Slawig
MaRDI profile type: Publication
full work available at URL: s00245-003-0787-1
OpenAlex ID: W2151874613
DOI: 10.1007/S00245-003-0787-1
description: scientific article; zbMATH DE number 2101891