Calculus of Variations and Geometric Measure Theory

M. Gori

On the lower semicontinuity of supremal functionals defined on measures

created on 04 Nov 2004
modified by gori on 27 Dec 2006


Published Paper

Inserted: 4 nov 2004
Last Updated: 27 dec 2006

Journal: Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat.
Volume: 9
Number: 2
Pages: 327-369
Year: 2006


In this paper we consider two particular classes of supremal functionals defined on Radon measures and we find necessary and sufficient conditions for their lower semicontinuity with respect to the weak$^*$ convergence. Some applications to the minimization of functionals defined on $BV$ are presented.

Keywords: Lower Semicontinuity, Dirichlet problem, Supremal functionals, level convexity