Regularity results for an optimal design problem with a volume constraint
Dipartimento di Ingegneria – Università del Sannio,
2 Department of Mathematical Sciences, Carnegie Mellon University, PA 15213-3890 Pittsburgh, USA
3 Università di Napoli “Federico II” Dipartimento di Mat. e Appl. ‘R. Caccioppoli’, Via Cintia, 80126 Napoli, Italy
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.
Mathematics Subject Classification: 49N15 / 49N60 / 49N99
Key words: Regularity / nonlinear variational problem / free interfaces
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