Sharp Hodge decompositions in two and three dimensional Lipschitz domains

Dorina Mitrea; Marius Mitrea

doi:10.1016/S1631-073X(02)02232-X

Sharp Hodge decompositions in two and three dimensional Lipschitz domains
[Décompositions de Hodge optimales pour les domaines lipschitziens en dimensions deux et trois]

Dorina Mitrea ¹ ; Marius Mitrea ¹

¹ Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA

Comptes Rendus. Mathématique, Volume 334 (2002) no. 2, pp. 109-112.

Résumé
Abstract

Nous identifionsla gamme optimale des coefficients s, p pour lesquels les formes différentielles à coefficients dans l'espace de Sobolev $L_{s}^{p} (Ω)$ admettent des décompositions de Hodge naturelles, pour des domaines lipschitziens $Ω$ arbitraires de dimensions deux et trois.

We identify the optimal range of coefficients s, p for which differential forms with coefficients in the Sobolev space $L_{s}^{p} (Ω)$ admit natural Hodge decompositions in arbitrary two and three dimensional Lipschitz domains $Ω$ .

Reçu le : 2001-09-20
Accepté le : 2001-12-03
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02232-X

Affiliations des auteurs :

Dorina Mitrea ¹ ; Marius Mitrea ¹

¹ Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA

@article{CRMATH_2002__334_2_109_0,
     author = {Dorina Mitrea and Marius Mitrea},
     title = {Sharp {Hodge} decompositions in two and three dimensional {Lipschitz} domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {109--112},
     publisher = {Elsevier},
     volume = {334},
     number = {2},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02232-X},
     language = {en},
}

TY  - JOUR
AU  - Dorina Mitrea
AU  - Marius Mitrea
TI  - Sharp Hodge decompositions in two and three dimensional Lipschitz domains
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 109
EP  - 112
VL  - 334
IS  - 2
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02232-X
LA  - en
ID  - CRMATH_2002__334_2_109_0
ER  -

%0 Journal Article
%A Dorina Mitrea
%A Marius Mitrea
%T Sharp Hodge decompositions in two and three dimensional Lipschitz domains
%J Comptes Rendus. Mathématique
%D 2002
%P 109-112
%V 334
%N 2
%I Elsevier
%R 10.1016/S1631-073X(02)02232-X
%G en
%F CRMATH_2002__334_2_109_0

Dorina Mitrea; Marius Mitrea. Sharp Hodge decompositions in two and three dimensional Lipschitz domains. Comptes Rendus. Mathématique, Volume 334 (2002) no. 2, pp. 109-112. doi : 10.1016/S1631-073X(02)02232-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02232-X/

Bibliographie
Cité par

[1] B. Dahlberg Arch. Rational Mech. Anal., 65 (1977), pp. 275-288

[2] B. Dahlberg; C. Kenig Ann. Math., 125 (1987), pp. 437-465

[3] R. Dautray; J.-L. Lions Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, 1990

[4] E. Fabes; M. Jodeit; N. Rivière Acta Math., 141 (1978), pp. 165-186

[5] V. Girault; P.-A. Raviart Finite Element Methods for Navier–Stokes Equations, Springer-Verlag, 1986

[6] Grachev N.V., Maz'ya V.G., Linköping Univ. Research Report LiTH-MAT-R-91-50

[7] D. Jerison; C.E. Kenig J. Functional Anal., 130 (1995), pp. 161-219

[8] M. Mitrea; M. Taylor J. Functional Anal., 176 (2000), pp. 1-79

[9] G. Schwarz Hodge Decomposition – A Method for Solving Boundary Value Problems, LMN, 1607, Springer-Verlag, 1995

[10] G. Verchota J. Functional Anal., 59 (1984), pp. 572-611

Cité par Sources :

Commentaires - Politique