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.

Capillarity problems with nonlocal surface tension energies / F. Maggi, E. Valdinoci. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 42:9(2017), pp. 1403-1446.

Capillarity problems with nonlocal surface tension energies

E. Valdinoci
2017

Abstract

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.
capillarity problems; nonlocal perimeter; regularity results; analysis; applied mathematics
Settore MAT/05 - Analisi Matematica
Elliptic Pdes and Symmetry of Interrfaces and Layers for Odd Nonlinearties
Aspetti variazionali e perturbativi nei problemi differenziali nonlineari
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/549544
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