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Regularity results for an optimal design problem with a volume constraint

Published online by Cambridge University Press:  07 March 2014

Menita Carozza ,
Irene Fonseca  and
Antonia Passarelli di Napoli
Menita Carozza
Affiliation:
Dipartimento di Ingegneria – Università del Sannio, Corso Garibaldi 82100 Benevento, Italy. carozza@unisannio.it
Irene Fonseca
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, PA 15213-3890 Pittsburgh, USA; fonseca@andrew.cmu.edu
Antonia Passarelli di Napoli
Affiliation:
Università di Napoli “Federico II” Dipartimento di Mat. e Appl. ‘R. Caccioppoli’, Via Cintia, 80126 Napoli, Italy; antpassa@unina.it
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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.

Keywords

Regularitynonlinear variational problemfree interfaces
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 2 , April 2014 , pp. 460 - 487
Copyright
© EDP Sciences, SMAI, 2014

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