Motivated by applications in fluid dynamics, we show elementarily that a nonnegative compactly supported Radon measure μ belongs to the negative Sobolev space provided that function is Hölder continuous. In passing we obtain embedding of the space of nondecreasing Hölder continuous functions on into the fractional Sobolev space . We comment on possible generalizations and numerical applications.
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 à condition que la fonction soit hölderienne. En passant, on obtient un plongement d'espace des fonctions croissantes hölderiennes sur dans l'espace de Sobolev fractionnaire . On discute des généralisations et des applications numériques.
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Grzegorz Jamróz 1
@article{CRMATH_2015__353_6_529_0, author = {Grzegorz Jamr\'oz}, title = {Nonnegative measures belonging to $ {H}^{-1}({\mathbb{R}}^{2})$}, journal = {Comptes Rendus. Math\'ematique}, pages = {529--534}, publisher = {Elsevier}, volume = {353}, number = {6}, year = {2015}, doi = {10.1016/j.crma.2015.04.010}, language = {en}, }
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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