## 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

### Keywords:

multigrid methods; shape design; smooth solutions
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### References:

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