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Publication 13-CNA-010

Regularity Results for an Optimal Design Problem with a Volume Constraint

Menita Carozza
Dipartimento di Ingegneria
Universita del Sannio
carozza@unisannio.it

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Antonia Passarelli
Dipartimento di Mat. e Appl. "R. Caccioppoli"
Universita di Napoli "Federico II"
antpassa@unina.it

Abstract: Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration ($u;E$), Hölder continuity of the function $u$ is proved as well as partial regularity of the boundary of the minimal set $E$. Moreover, full regularity of the boundary of the minimal set is obtained under suitable closeness assumptions on the eigenvalues of the bulk energies.

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