Publication 18-CNA-008
Equilibria configurations for
epitaxial crystal growth with adatoms
Marco Caroccia
Faculdade de Ciencias, Departamento de Matemática
Universidade de Lisboa
Lisboa, Portugal
Riccardo Cristoferi
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh PA 15213-3890 USA
rcristof@andrew.cmu.edu
Laurent Dietrich
Lycée Fabert, Batiment Toqueville (CPGE)
57000 Metz, France
Abstract: The behavior of a surface energy $\mathcal{F}(E, u)$, where $E$ is a set of finite perimeter
and u $\in$ $L^1$($\delta$*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 difusing 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. This is part of an ongoing project
aimed at an analytical study of diffuse interface approximations of the associated
evolution equations.
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