Lower semicontinuity of variational integrals on elliptic complexes
Volume 204 / 2011
Studia Mathematica 204 (2011), 283-294
MSC: Primary 49N60; Secondary 49N99.
DOI: 10.4064/sm204-3-7
Abstract
We prove a lower semicontinuity result for variational integrals associated with a given first order elliptic complex, extending, in this general setting, a well known result in the case $ {\cal D}^{\prime}(\mathbb R^n,\mathbb R) \xrightarrow {\nabla} {\cal D}^{\prime}(\mathbb R^n,\mathbb R^n) \xrightarrow {\rm curl} {\cal D^{\prime}}(\mathbb R^n,\mathbb R^{n\times n}). $
