Calculus of Variations and Geometric Measure Theory

M. Gori - F. Maggi

The common root of the geometric conditions in Serrin's lower semicontinuity theorem

created on 29 Jul 2002
modified by maggi on 19 Dec 2005


Published Paper

Inserted: 29 jul 2002
Last Updated: 19 dec 2005

Journal: Ann. Mat. Pura Appl. (4)
Volume: 184
Number: 1
Pages: 95-114
Year: 2005


In this paper we extend a classical lower semicontinuity theorem by J. Serrin. We achieve this result applying an approximation method for convex functions where, instead of supporting hyperplanes, certain maximal cones are considered. This allows also to give the characterization of the class of functions that can be written as the supremum of strictly convex ones.

Keywords: relaxation, demicoercivity, Lower Semicontinuity, convexity, strict convexity