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ON THE LOWER SEMICONTINUITY OF QUASICONVEX INTEGRALS

In this paper, dedicated to Neil Trudinger in the occasion of his 70 th birthday, we propose a relatively elementary proof of the weak lower semicontinuity in W 1,p of a general integral of the Calculus of Variations of the type (1.1) below with a quasiconvex density function satisfying p-growth conditions. Several comments and references on the related literature, and a subsection devoted to some properties of the maximal function operator, are also included.