Abstract

We consider shape optimization problems of the form min⁡{∫∂Af(x,ν(x)) dHn−1:A∈A}\min\{\int_{\partial A} f(x,\nu(x))\,\mathrm{d}\mathcal{H}^{n-1} : A \in \mathcal{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.

Author information

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Giuseppe Buttazzo

Dipartimento di Matematica, Via Buonarroti 2, 56127 Pisa, Italy

Paolo Guasoni

Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy

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Suggested citation

G. Buttazzo, P. Guasoni. “Shape Optimization Problems over Classes of Convex Domains.” Journal of Convex Analysis 4 (1997), No. 2, 343–351. https://doi.org/10.68381/jca04019

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Published by Heldermann Verlag, 1997. Rights now held by Banach Press LLC.