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.
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Buliga, M. Lower semi-continuity of integrals with G-quasiconvex potential. Z. angew. Math. Phys. 53, 949–961 (2002). https://doi.org/10.1007/PL00012621
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DOI: https://doi.org/10.1007/PL00012621