Weak-strong uniqueness for measure-valued solutions in quasiconvex elastodymanics

A weak-strong uniqueness result is presented for a class of measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty of this work is that the underlying stored-energy function is assumed strongly quasiconvex, a natural condition in elasticity, yet one not amenable to typical techniques in hyperbolic theory which are based on convexity. The proof borrows tools from the calculus of variations to prove a Garding-type inequality for quasiconvex functions, and recasts them to adapt the relative entropy method to quasiconvex energies. The work is joint with Stefano Spirito (University of L’Aquila).

Contact person: Virginia Agostiniani