Regularity results for an optimal design problem with lower order terms

Abstract We study the regularity of interface for optimal energy configurations functionals involving bulk energies with an additional perimeter penalization interface. Here we allow a more general structure functional in term. For minimal configuration ( E , u stretchy="false">) {(E,u)} , Hölder continuity u is well known. give estimate singular set boundary ∂ ⁡ {\partial E} . Namely show that Hausdorff dimension strictly smaller than n - 1 {n-1}