Calculus of Variations and Geometric Measure Theory

M. Focardi - P. Marcellini

On The Lower Semicontinuity Of Quasiconvex Integrals

created by focardi on 29 May 2014


Published Paper

Inserted: 29 may 2014
Last Updated: 29 may 2014

Journal: Bulletin of the Institute of Mathematics Academia Sinica
Volume: 9
Number: 2
Pages: 245--266
Year: 2014


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