PIRE - mathematics, mechanics, materials science

Science at the triple point between
mathematics, mechanics and materials science

Publication 90

Regularity Results for an Optimal Design Problem with a Volume Constraint


Menita Carozza
Dipartimento di Ingegneria
Universita del Sannio

CMUIrene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Antonia Passarelli
Dipartimento di Mat. e Appl. "R. Caccioppoli"
Universita di Napoli "Federico II"

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.
Get the paper in its entirety

Back to Publications