Calculus of Variations and Geometric Measure Theory
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M. Caroccia - R. Cristoferi - L. Dietrich

Equilibria configurations for epitaxial crystal growth with adatoms

created by caroccia on 27 Oct 2017

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Submitted Paper

Inserted: 27 oct 2017
Last Updated: 27 oct 2017

Year: 2017

Abstract:

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.


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