Authors
Citation
M. Moussaoui, H (DIV, ROT, OMEGA) SPACES IN A PLANE POL YGONAL DOMAIN, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 322(3), 1996, pp. 225-229
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
07644442
Volume
322
Issue
3
Year of publication
1996
Pages
225 - 229
Database
ISI
SICI code
0764-4442(1996)322:3<225:H(ROSI>2.0.ZU;2-4
Abstract
For a plane polygonal domain Omega with boundary Gamma we compare the
two spaces: V = {(u) over right arrow is an element of H-1 (Omega)(2);
(u) over right arrow . (n) over right arrow = O on Gamma} and W = {(u
) over right arrow is an element of L(2) (Omega)(2); div (u) over righ
t arrow is an element of L(2) (Omega), (u) over right arrow . (n) over
right arrow = O on Gamma} We prove that V = W iff Omega is convex. Ot
herwise V is a finite codimensional closed subspace of W and we give t
he dimension and a basis of its orthogonal.