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Journal of Convex Analysis, Vol. 4, No. 2, pp. 343-351 (1997)
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Shape Optimization Problems over Classes of Convex Domains

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Giuseppe Buttazzo and Paolo Guasoni

Dipartimento di Matematica, Via Buonarroti 2, 56127 Pisa, Italy, buttazzo@sab.sns.it, and Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy, guasoni@cibs.sns.it

**Abstract:** We consider shape optimization problems of the form

\min\left\{\int_{\partial A} f(x,\nu(x))\hbox{d}x {\cal{H}^{n-1}} :A\in{\cal A}\right\}

where $f$ is any continuous function and the class ${\cal A}$ 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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