Geodesic
Sobolev spaces of integer order on compact homogeneous manifolds and invariant differential operators
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 4, pp. 219-233.

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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 \( M \). 
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     title = {Sobolev spaces of integer order on compact homogeneous	manifolds and invariant differential operators},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Bondioli, Cristiana. Sobolev spaces of integer order on compact homogeneous	manifolds and invariant differential operators. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 7 (1996) no. 4, pp. 219-233. https://geodesic-test.mathdoc.fr/item/RLIN_1996_9_7_4_a2/

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