Comptes Rendus
no. 6
Partial differential equations/Functional analysis
Nonnegative measures belonging to H−1(R2)
[Les mesures positives appartenantes à H−1(R2)]

Présenté par : Jean-Michel Coron

Grzegorz Jamróz1
1 Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland
Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 529-534.

En vue d'applications en mécanique des fluides, on démontre qu'une mesure positive de Radon à support compact appartient à l'espace négatif de Sobolev H−1(R2) à condition que la fonction r↦μ(B(0,r)) soit hölderienne. En passant, on obtient un plongement d'espace des fonctions croissantes hölderiennes sur R dans l'espace de Sobolev fractionnaire H1/2(R). On discute des généralisations et des applications numériques.

Motivated by applications in fluid dynamics, we show elementarily that a nonnegative compactly supported Radon measure μ belongs to the negative Sobolev space H−1(R2) provided that function r↦μ(B(0,r)) is Hölder continuous. In passing we obtain embedding of the space of nondecreasing Hölder continuous functions on R into the fractional Sobolev space H1/2(R). We comment on possible generalizations and numerical applications.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.04.010

Grzegorz Jamróz 1

1 Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland 
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Grzegorz Jamróz. Nonnegative measures belonging to $ {H}^{-1}({\mathbb{R}}^{2})$. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 529-534. doi : 10.1016/j.crma.2015.04.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.010/

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