Analysis and numerical studies of a problem of shape design
The paper deals with the following problem of shape design: (P) minimize \(J(v)=\int_{\Omega}\{g(| \nabla v|)-v\}dx\) on \(W_ 0^{1,2}(\Omega)\), where \(\Omega \subset {\mathbb{R}}^ N\) is a bounded simply connected domain, \(N\geq 2\). The uniqueness for smooth solutions to (P) is studied and some numerical methods are applied to verify certain analytical results.
scientific article; zbMATH DE number 4199503
scientific article