Calculus of Variations and Geometric Measure Theory

M. Caroccia - R. Cristoferi - L. Dietrich

Equilibria configurations for epitaxial crystal growth with adatoms

created by caroccia on 27 Oct 2017
modified on 15 May 2018


Published Paper

Inserted: 27 oct 2017
Last Updated: 15 may 2018

Journal: Archive for Rational Mechanics and Analysis
Pages: 1-54
Year: 2018
Doi: 10.1007/s00205-018-1258-9


The behavior of a surface energy $\mathcal{F}(E,u)$, where $E$ is a set of finite perimeter and $u\in L^1(\partial^* E, \mathbb{R}_+)$ is studied. These energies have been recently considered in the context of materials science to derive a new model in crystal growth that takes into account the effect of atoms freely diffusing on the surface (called adatoms), which are responsible for morphological evolution through an attachment and detachment process. Regular critical points, existence and uniqueness of minimizers are discussed and the relaxation of $\mathcal{F}$ in a general setting under the $L^1$ convergence of sets and the vague convergence of measures is characterized.