Superposition with subunitary powers in Sobolev spaces
Résumé
Let $0$<$a$<$1$ and set $\Phi (t)=|t|^a$, $t\in {\mathbb R}$. We prove that the superposition operator $u\mapsto \Phi (u)$ maps the Sobolev space $W^{1,p}({\mathbb R}^n)$ into the fractional Sobolev space $W^{a,p/a}({\mathbb R}^n)$. We also investigate the case of more general nonlinearities.
Domaines
Analyse classique [math.CA]Origine | Fichiers produits par l'(les) auteur(s) |
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