Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Luca Esposito

Dip. di Matematica e Informatica, Università di Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

luesposi@unisa.it

Nicola Fusco

Dip. di Matematica e Applicazioni, Università di Napoli, Via Cintia, 80126 Napoli, Italy

n.fusco@unina.it

Keywords

  • Perimeter penalization
  • volume constraint
  • regularity

Mathematics Subject Classification

49N60, 49Q20

Suggested citation

L. Esposito, N. Fusco. “A Remark on a Free Interface Problem with Volume Constraint.” Journal of Convex Analysis 18 (2011), No. 2, 417–426.

Copyright Banach Press 2011