Variational problems involving nonlocal perimeter and prescribed nonlocal mean curvature problems
アブストラクト
We consider a geometric minimization problem arising from a model of liquid drops at equilibrium when a long-range interaction between particles exists. The energy in the problem consists of two terms: a nonlocal perimeter, which is a “nonlocal” counterpart of classical perimeter, and a potential term. We explain that a minimizer in our problem always exists if a potential energy is coercive and is convex when its volume is sufficiently small. Moreover, we present a nonlocal version of prescribed mean curvature problem and will see an analogy between the classical and nonlocal problems. This talk is partially based on a joint work with K. Bessas and M. Novaga.