Analysis and numerical studies of a problem of shape design. (English) Zbl 0726.65071

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.


65K10 Numerical optimization and variational techniques
49M27 Decomposition methods
49J40 Variational inequalities
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