Functionals depending on curvatures with constraints
Maria Giovanna Mora, Massimiliano Morini
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.
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