On The Lower Semicontinuity Of Quasiconvex Integrals
by Paolo Marcellini   Matteo Focardi  

Vol. 9 No. 2 (2014) P.245~P.266

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.

KEYWORDS
Quasiconvex integrals, lower semicontinuity

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 49J45; 49K20

MILESTONES

Received: 2013-07-21
Revised :
Accepted: 2014-04-06

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