Resumen de Intrinsic colocal weak derivatives and Sobolev spaces between manifolds

Alexandra Convent, Jean van Schaftingen

• 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.