Ce livre est une initiation aux approches modernes de l'optimisation mathématique de
formes. Il s' appuie sur les seules connaissances de première année de Master de …

Strained epitaxial films grown on a relatively thick substrate are considered in the context of
plane linear elasticity. The total free energy of the system is assumed to be the sum of the …

We describe the phase-field method, a new approach to optimal design originally introduced
in Bourdin and Chambolle (2000, 2003). It is based on the penalization of the variation of the …

We consider a variational model introduced in the physical literature to describe the epitaxial
growth of an elastic film over a thick flat substrate when a lattice mismatch between the two …

We present here an analysis of the regularity of minimizers of a variational model for
epitaxially strained thin-films. The regularity of energetically-optimal film profiles is studied …

This work discusses the role of highly anisotropic interfacial energy for problems involving a
material void in a linearly elastic solid. Using the calculus of variations it is shown that …

We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian
operator among sets of given perimeter. In two dimensions, we prove that the optimum …

We consider a variational model related to the formation of islands in heteroepitaxial growth
on unbounded domains. We first derive the scaling regimes of the minimal energy in terms …

Derivation of a heteroepitaxial thin-film model Page 1 Interfaces and Free Boundaries 22 (2020),
1–26 DOI 10.4171/IFB/435 Derivation of a heteroepitaxial thin-film model ELISA DAVOLI …

Inside a fixed bounded domain $\Omega $ of the plane, we look for the best compact
connected set $ K $, of given perimeter, in order to maximize the first Dirichlet eigenvalue …