Calculus of Variations and Geometric Measure Theory

M. Focardi - N. Fusco - C. Leone - P. Marcellini - E. Mascolo - A. Verde

Weak lower semicontinuity for polyconvex integrals in the limit case

created by focardi on 14 Feb 2013
modified on 26 Feb 2015


Published Paper

Inserted: 14 feb 2013
Last Updated: 26 feb 2015

Journal: Calc. Var. Partial Differential Equations
Volume: 51
Number: 1-2
Pages: 171-193
Year: 2014
Doi: 10.1007/s00526-013-0670-0


We prove a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps $u:\Omega\subset\mathbb{R}^n\to\mathbb{R}^m$ in $W^{1,m}$, $2\leq m \leq n$, bounded in $W^{1,m−1}$ and convergent in $L^1$ under mild technical conditions but without any extra coercivity assumption on the integrand.

Keywords: Polyconvexity, Lower Semicontinuity, non-coercive integrand