Functionals depending on curvatures with constraints

Abstract

We deal with a family of functionals depending on curvatures and we prove for them compactness and semicontinuity properties in the class of closed and bounded sets which satisfy a uniform exterior and interior sphere condition. We apply the results to state an existence theorem for the Nitzberg and Mumford problem under this additional constraint.Comment: 20 pages. To appear on Rendiconti del Seminario Matematico dell'Universita' di Padov