Gains of integrability and local smoothing effects for quadratic evolution equations
Résumé
We characterize geometrically the semigroups generated by non-selfadjoint quadratic differential operators $(e^{-tq^w})_{t\geq 0}$ enjoying local smoothing effects and providing gains of integrability. More precisely, we prove that the evolution operators $e^{-tq^w}$ map $L^{\mathfrak{p}}$ on $L^{\mathfrak{q}} \cap C^\infty$, for all $1\leq \mathfrak{p} \leq \mathfrak{q} \leq \infty$, if and only if the singular space of the quadratic operator $q^w$ is included in the graph of a linear map. We also provide quantitative estimates for the associated operator norms in the short-time asymptotics $0
Origine : Fichiers produits par l'(les) auteur(s)
Joackim Bernier : Connectez-vous pour contacter le contributeur
https://hal.science/hal-03437144
Soumis le : vendredi 19 novembre 2021-17:06:41
Dernière modification le : lundi 11 mars 2024-14:28:41
Archivage à long terme le : dimanche 20 février 2022-21:06:28
Citer
Paul Alphonse, Joackim Bernier. Gains of integrability and local smoothing effects for quadratic evolution equations. 2021. ⟨hal-03437144v1⟩
Collections
63
Consultations
39
Téléchargements