On the curl operator and some characterizations of matrix fields in Lipschitz domains

As well-known, De Rham's Theorem is a classical way to characterize vector fields as the gradient of scalar fields, it tool great importance in theory fluids mechanic. The first aim this paper provide useful rotational version theorem establish several results on boundary value problems field electromagnetism. Gurtin presented completeness Beltrami's representation smooth domains for symmetric matrix. extension was obtained by Geymonat and Krasucki when domain ? only Lipschitz matrix Ls2(?). Our second present new extensions domains, firstly case where data are Ds(?) secondly Wsm,r(?). third objective extend Saint-Venant's distributions.