Lower semi-continuity of integrals with G-quasiconvex potential

Abstract.

This paper introduces the proper notion of variational quasiconvexity associated to a group of bi-Lipschitz homeomorphisms, with possible applications in elasticity. We prove a lower semicontinuity theorem connected to this notion, which improves a result of Dacorogna and Fusco [7]. In the second part of the paper we apply this result to a class of functions, introduced in [5]. Such functions are GL(n, R)⁺ quasiconvex, hence they induce lower semicontinuous integrals.