Non-local Minimal Surfaces
نویسندگان
چکیده
In this paper we study the geometric properties, existence, regularity and related issues for a family of surfaces which are boundaries of sets minimizing certain integral norms. These surfaces can be interpreted as a non-infinitesimal version of classical minimal surfaces. Our work is motivated by the structure of interphases that arise in classical phase field models when very long space correlations are present. Motion by mean curvature is obtained classically in two different ways. One way is as an asymptotic limit of phase field models involving a double well potential, that is as the steepest descent of the Ginzburg-Landau energy functional
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