$\mathcal{A}$-Quasiconvexity, Gårding Inequalities, and Applications in PDE Constrained Problems in Dynamics and Statics

A Gårding-type inequality is proved for a quadratic form associated to $\mathcal{A}$-quasiconvex functions. This appears as the relative entropy in theory of conservation laws and it related Weierstrass excess function calculus variations. The former provides weak-strong uniqueness results, whereas latter has been used provide sufficiency theorems local minimizers. Using this new Gårding we an extension these results PDE constrained problems dynamics statics under $\mathcal{A}$-quasiconvexity assumptions. application improves existing by proving $L^p$-local minimizers classical $\mathcal{A}={curl}$ case.