2016/06/28 by Francesco Maggi, Enrico Valdinoci, Maggi, Francesco +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #math-ph #math.AP #math.MP #math.OC
paper · pdf · doi:10.48550/arxiv.1606.08610
37 pages, 4 figures
arxiv created 2016/06/28 · arxiv updated 2016/06/29
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.