Calculus of Variations and Geometric Measure Theory

F. Maggi - E. Valdinoci

Capillarity problems with nonlocal surface tension energies

created by maggi on 28 Jun 2016
modified on 25 Apr 2018



Inserted: 28 jun 2016
Last Updated: 25 apr 2018

Journal: Comm. PDE
Year: 2017

37 pages, 4 figures


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.