Affiliation:
1. Dipartimento di Matematica , Università degli Studi di Salerno , Fisciano , Italy
Abstract
Abstract
We study the regularity of the interface for optimal energy configurations of functionals involving bulk energies with an additional perimeter penalization of the interface. Here we allow a more general structure for the energy functional in the bulk term. For a minimal configuration
(
E
,
u
)
{(E,u)}
, the Hölder continuity of u is well known. We give an estimate for the singular set of the boundary
∂
E
{\partial E}
. Namely we show that the Hausdorff dimension of the singular set is strictly smaller than
n
-
1
{n-1}
.
Subject
Applied Mathematics,Analysis
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