# Lower semicontinuity for polyconvex integrals without coercivity assumptions

created by decicco on 19 Nov 2013
modified on 25 Nov 2013

[BibTeX]

Accepted Paper

Inserted: 19 nov 2013
Last Updated: 25 nov 2013

Journal: Evolution Equations and Control Theory (EECT)
Year: 2013

Abstract:

We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to maps $u:\Omega \subset \mathbb{R}^{n}\rightarrow \mathbb{R}^{m}$ in $W^{1,n}(\Omega ;\mathbb{R}^{m})$ with $n\geq m\geq 2$, with respect to the weak $W^{1,p}$-convergence for $p>m-1$, without assuming any coercivity condition.