Sobolev spaces of integer order on compact homogeneous	manifolds and invariant differential operators

Bondioli, Cristiana

Sobolev spaces of integer order on compact homogeneous manifolds and invariant differential operators

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996), p. 219-233 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

Let $M$ be a Riemannian manifold, which possesses a transitive Lie group $G$ of isometries. We suppose that $G$ , and therefore $M$ , are compact and connected. We characterize the Sobolev spaces $W_{p}^{1} (M)$ $(1 < p < + \infty)$ by means of the action of $G$ on $M$ . This characterization allows us to prove a regularity result for the solution of a second order differential equation on $M$ by global techniques.

Sia $M$ una varietà riemanniana, dotata di un gruppo di Lie $G$ transitivo di isometrie. Si suppone che $G$ , e pertanto $M$ , siano compatti e connessi. Si caratterizzano gli spazi di Sobolev $W_{p}^{1} (M)$ $(1 < p < + \infty)$ tramite l'azione di $G$ su $M$ . Questa caratterizzazione permette di dimostrare tramite tecniche globali un risultato di regolarità per la soluzione di un'equazione differenziale del secondo ordine su $M$ .

Publié le : 1996-12-01

MR 1454416 | Zbl 0938.46031

@article{RLIN_1996_9_7_4_219_0,
     author = {Cristiana Bondioli},
     title = {Sobolev spaces of integer order on compact homogeneous	manifolds and invariant differential operators},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {7},
     year = {1996},
     pages = {219-233},
     zbl = {0938.46031},
     mrnumber = {1454416},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1996_9_7_4_219_0}
}

Bondioli, Cristiana. Sobolev spaces of integer order on compact homogeneous	manifolds and invariant differential operators. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 7 (1996) pp. 219-233. http://gdmltest.u-ga.fr/item/RLIN_1996_9_7_4_219_0/

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