Let and set , . Let and . We prove that the superposition operator maps the Sobolev space into the fractional Sobolev space . We also investigate the case of more general nonlinearities.
Pour , soit , . Soient et . Nous montrons que l'opérateur de superposition envoie l'espace de Sobolev dans l'espace de Sobolev fractionnaire . Nous examinons aussi la superposition avec des non-linéarités plus générales.
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Petru Mironescu 1
@article{CRMATH_2015__353_6_483_0, author = {Petru Mironescu}, title = {Superposition with subunitary powers in {Sobolev} spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {483--487}, publisher = {Elsevier}, volume = {353}, number = {6}, year = {2015}, doi = {10.1016/j.crma.2015.03.020}, language = {en}, }
Petru Mironescu. Superposition with subunitary powers in Sobolev spaces. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 483-487. doi : 10.1016/j.crma.2015.03.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.020/
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[2] Theory of Function Spaces, Monographs in Mathematics, vol. 78, Birkhäuser Verlag, Basel, Switzerland, 1983
[3] L. Véron, personal communication.
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