Rigidity estimates, besides their inherent geometric interest, have played a prominent role in the mathematical study of models related to elasticity\plasticity. For instance, the celebrated rigidity estimate of Friesecke, James, and Müller has been widely used in problems related to linearization, discrete-to-continuum or dimension-reduction issues within the framework of nonlinear elasticity.
In this talk I will present a generalization of this result to the setting of variable domains, where the geometry of the domain comes into play in terms of a suitable surface energy of its boundary.
As an application, we rigorously derive linearized models for nonlinearly elastic materials with free surfaces by means of Γ-convergence.
This is joint work with Manuel Friedrich and Leonard Kreutz.