Capillarity problems with nonlocal surface tension energies
  We explore the possibility of modifying the classical Gauss free energy functional used in capillarity theory by considering surface tension energies of nonlocal type. The corresponding variational principles lead to new equilibrium conditions which are compared to the mean curvature equation and Young's law found in classical capillarity theory. As a special case of this family of problems we recover a nonlocal relative isoperimetric problem of geometric interest. 
Francesco Maggi and Enrico Valdinoci
math.AP math-ph math.MP math.OC