Intrinsic colocal weak derivatives and Sobolev spaces between manifolds

• Alexandra Convent ^[1] ; Jean Van Schaftingen ^[1]
  1. [1] Université Catholique de Louvain

     Université Catholique de Louvain

     Arrondissement de Nivelles, Bélgica

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 16, Nº 1, 2016, págs. 97-128
• Idioma: inglés
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• Resumen

  • We define the notion of co-locally weakly differentiable maps from a manifold M to a manifold N. If p ! 1 and if the manifolds M and N are endowed with a Riemannian metric, this allows us to define intrinsically the homogeneous Sobolev space W˙ 1,p(M, N). This new definition is equivalent to the definition by embedding in the Euclidean space and to that of Sobolev map into a metric space.

    The co-local weak derivative is an approximate derivative. The co-local weak differentiability is stable under a suitable weak convergence. The Sobolev spaces can be endowed with various intrinsic distances that induce the same topology and for which the space is complete.