Lower semicontinuity of variational integrals on elliptic complexes

Anna Verde¹

¹ Dipartimento di Matematica Università degli Studi di Napoli “Federico II” via Cintia 80126 Napoli, Italy

Studia Mathematica, Tome 204 (2011) no. 3, pp. 283-294

Résumé

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}). $

Détail

DOI : 10.4064/sm204-3-7

Keywords: prove lower semicontinuity result variational integrals associated given first order elliptic complex extending general setting known result cal prime mathbb mathbb xrightarrow nabla cal prime mathbb mathbb xrightarrow curl cal prime mathbb mathbb times