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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_1996_9_7_4_a2,
     author = {Bondioli, Cristiana},
     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},
     pages = {219--233},
     year = {1996},
     volume = {Ser. 9, 7},
     number = {4},
     zbl = {0938.46031},
     mrnumber = {MR1454416},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_4_a2/}
}
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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. http://geodesic.mathdoc.fr/item/RLIN_1996_9_7_4_a2/