Capillarity problems with nonlocal surface tension energies
- Maggi, Francesco
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 76B45 35R11 49K21
- nonlocal perimeter functional, long range particle interactions, capillarity phenomena, Young's law
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.
- Commun. Partial Differential Equations, 42:9 (2017) pp. 1403--1446.