Symétrisations indépendantes du temps pour certains opérateurs du type de Schrödinger. I

Takeuchi, Jiro

Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 1-53 / Harvested from Biblioteca Digitale Italiana di Matematica

Résumé

Si danno condizioni sufficienti e condizioni necessarie affinché il problema di Cauchy per alcuni operatori di tipo Schrödinger sia ben posto in spazi di Sobolev. Gli operatori qui considerati sono operatori di Schrödinger con potenziali vettoriali complessi, una generalizzazione degli operatori di 2-evoluzione nel senso di Petrowsky, e alcuni sistemi tipo Leray-Volevich di operatori lineari a derivate parziali. Il metodo che usiamo in questo articolo è la simmetrizazione $L^{2}$ degli operatori non dipendenti dal tempo, che abbiamo già usato nelle Note [52]-[54].

Abstract

We give sufficient conditions and necessary conditions for the Cauchy problem for certain operators of Schrödinger type to be well posed in the Sobolev spaces. Operators of which we treat are Schrödinger operators with complex-valued vector potentials, those generalizations to 2-evolution operators in the sense of Petrowsky and certain Leray-Volevich systems of linear partial differential operators. The method that we use in this article is time-independent $L^{2}$-symmetrization of operators which has been proposed in our Notes [52] to [54].

Détail

Publié le : 2002-02-01

MR 1881443 | Zbl 1121.35119

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