EQUILIBRIUM CONFIGURATIONS FOR NONHOMOGENEOUS LINEARLY ELASTIC MATERIALS WITH SURFACE DISCONTINUITIES

Antonin Chambolle (1) , Vito Crismale (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We prove a compactness and semicontinuity result that applies to minimisation problems in nonhomogeneous linear elasticity under Dirichlet boundary conditions. This generalises a previous compactness theorem that we proved and employed to show existence of minimisers for the Dirichlet problem for the (homogeneous) Griffith energy.

Domaines: Mathématiques [math]; Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Antonin Chambolle, Vito Crismale. EQUILIBRIUM CONFIGURATIONS FOR NONHOMOGENEOUS LINEARLY ELASTIC MATERIALS WITH SURFACE DISCONTINUITIES. 2020. ⟨hal-02667936v1⟩