Inserted: 29 may 2014
Last Updated: 29 may 2014
Journal: Bulletin of the Institute of Mathematics Academia Sinica
In this paper, dedicated to Neil Trudinger in the occasion of his 70th birthday, we propose a relatively elementary proof of the weak lower semicontinuity in W1; 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.
Keywords: Lower Semicontinuity, Quasiconvex integrals