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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.

MSC:

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