Archive for Rational Mechanics and Analysis

, Volume 230, Issue 3, pp 785–838 | Cite as

Equilibria Configurations for Epitaxial Crystal Growth with Adatoms

  • Marco Caroccia
  • Riccardo Cristoferi
  • Laurent Dietrich


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, the freely diffusing on the surface (called adatoms), which are responsible for morphological evolution through an attachment and detachment process. Regular critical points, the existence and uniqueness of minimizers are discussed and the relaxation of \({\mathcal{F}}\) in a general setting under the L1 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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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  3. 3.Lycée Fabert, Bâtiment Toqueville (CPGE)MetzFrance

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