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Journal of Convex Analysis 18 (2011), No. 2, 417--426
Copyright Heldermann Verlag 2011

A Remark on a Free Interface Problem with Volume Constraint

Luca Esposito
Dip. di Matematica e Informatica, UniversitÓ di Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Nicola Fusco
Dip. di Matematica e Applicazioni, UniversitÓ di Napoli, Via Cintia, 80126 Napoli, Italy

We study the optimal design problem of finding the minimal energy configuration for a mixture of two conducting materials with a perimeter penalization of the unknown domain, when a volume constraint is added. We prove that minimizers of the constrained problem also minimize an unconstrained problem with a volume penalization for which regualarity results are available in the literature.

Keywords: Perimeter penalization, volume constraint, regularity.

MSC: 49N60, 49Q20

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