DOI: 10.68381/jca04019 ISSN: 0944-6532

Shape Optimization Problems over Classes of Convex Domains

Giuseppe Buttazzo, Paolo Guasoni
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We consider shape optimization problems of the form

\min\{\int_{\partial A} f(x,\nu(x))\,\mathrm{d}\mathcal{H}^{n-1} : A \in \mathcal{A}\} min ⁡ { ∫ ∂ A f ( x , ν ( x ) )   d H n − 1 : A ∈ A }
, where f is any continuous function and the class 𝒜 of admissible domains is made of convex sets. We prove the existence of an optimal solution provided the domains satisfy some suitable constraints.

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