Yury Grabovsky, Temple University
Abstract: The seminal work of Emmy Noether linked symmetries of variational functionals with conservation laws. Examining Noether's ideas, we show that they work just as well when transformations do not leave variational functionals invariant, but change them in quantifiable ways, which we refer to as partial symmetries. The corresponding identities, we call partial conservation laws, can be powerful tools in a wide variety of applications. One delivers Pohozaev-type identities to prove uniqueness of trivial solutions of nonlinear systems of PDEs, another---Clapeyron-like theorems for nonlinear elasticity. We demonstrate the utility of the latter for deriving a new formula for the energy release due to formation of an infinitesimal cavity in a nonlinearly elastic solid. This is a joint work with Lev Truskinovsky, ESPCI, Paris.