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.

Abstract (VO)
Résumé

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 $Ω$ .

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.

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

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     title = {Sharp {Hodge} decompositions in two and three dimensional {Lipschitz} domains},
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     doi = {10.1016/S1631-073X(02)02232-X},
     language = {en},
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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/

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Emilio Marmolejo-Olea; I. Mitrea; D. Mitrea; M. Mitrea Radiation conditions and integral representations for Clifford algebra-valued null-solutions of the Helmholtz operator, Journal of Mathematical Sciences (New York), Volume 231 (2018) no. 3, pp. 367-472 | DOI:10.1007/s10958-018-3826-9 | Zbl:1395.78015
M. Ballesteros; L. Menrath; Ma. de los Á. Sandoval-Romero; F. Torres-Ayala Besov and Triebel-Lizorkin regularity for the Hodge decomposition and applications to magnetic potentials, Journal of Mathematical Analysis and Applications, Volume 445 (2017) no. 1, pp. 532-555 | DOI:10.1016/j.jmaa.2016.07.070 | Zbl:1351.58002
W. Sprössig On Helmholtz decompositions and their generalizations - an overview, Mathematical Methods in the Applied Sciences, Volume 33 (2010) no. 4, pp. 374-383 | DOI:10.1002/mma.1212 | Zbl:1193.30071

Cité par 3 documents. Sources : zbMATH

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