Calculus of Variations and Geometric Measure Theory

G. De Philippis - S. Di Marino - M. Focardi

Lower semicontinuity for non-coercive polyconvex integrals in the limit case

created by focardi on 24 Feb 2014
modified on 17 Dec 2018


Published Paper

Inserted: 24 feb 2014
Last Updated: 17 dec 2018

Journal: Proceedings of the Royal Society of Edinburgh
Volume: 146A
Pages: 243--264
Year: 2016


Lower semicontinuity results for polyconvex functionals of the Calculus of Variations along sequences of maps $u:{\mathbb{R}}^n\to{\mathbb{R}}^m$ in $W^{1,m}$, $2\leq m\leq n$, weakly converging in $W^{1,m-1}$ are established.

In addition, for $m = n + 1$, we also consider the autonomous case for weakly converging maps in $W^{1,n-1}$.