Semicontinuity of a functional depending on curvature

In this paper we prove a lower semicontinuity result for a functional , defined on a class of bounded subsets of with a piecewise boundary, with respect to the -convergence of the sets. The functional depends on the curvature of in a linear way and contains a penalizing term which prevents the appearance of thin sets in the symmetric difference , where in an -approximating sequence of . Received: 3 January 2001 / Accepted: 11 May 2001 / Published online: 19 October 2001