Numerical Minimization of Functionals with Curvature by Convex Approximations

摘要

The authors address the numerical minimization of the functional F. It is wellknown that any minimum of F is the characteristic function of a set A contained in Omega whose boundary has prescribed mean curvature kappa and contact angle arc cos(mu) and boundry of Omega. The minimization of the functional F is just viewed as a model of geometrical type problems in the calculus of variations, that involve unknown interfaces and the related surface energy. Such problems may arise in important applicative fields, such as phase transition theories and computer vision theory, and their numerical solution seems quite difficult, because of the lack of convexity and regularity of the functionals at hand.