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Relaxation of surface energies with density

Banff International Research Station for Mathematical Innovation and Discovery

We study the behavior of surface energies defined over couples (E,u) where E is a set and u is a density on the boundary of E. Such energies have been considered in the context of materials science for modelling surface diffusion in a way that takes into consideration explicitly the effect of the free atoms moving on the surface (adatoms) in a regime where the elastic energy is negligible. We discuss regular critical points, existence and uniqueness of minimizers and we characterize the relaxation of the energy functional in a suitable topology. Finally, we will present approximations with phase field and discrete energy. This is a work in collaboration with Marco Caroccia and Laurent Dietrich

Mathematics; Calculus of variations and optimal control; optimization; Partial differential equations

video/mp4

Author affiliation: Carnegie Mellon University

2019-03-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69002

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/