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 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.
On the lower semicontinuity of quasiconvex integrals / Matteo Focardi; Paolo Marcellini. - In: BULLETIN OF INSTITUTE OF MATHEMATICS, ACADEMIA SINICA. NEW SERIES. - ISSN 2304-7909. - STAMPA. - 9:(2014), pp. 245-265.
On the lower semicontinuity of quasiconvex integrals
FOCARDI, MATTEO;MARCELLINI, PAOLO
2014
Abstract
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 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.
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