Intrinsic co-local weak derivatives and Sobolev spaces between manifolds (Q2809281)

The authors define and study co-locally weakly differentiable maps from a manifold \(M\) to a manifold \(N\). The paper is organized into four sections, as follows: 1. Co-locally weakly differentiable maps and co-local weak derivative (weak differentiability on a differentiable manifold, properties of the co-local weak derivative, approximate differentiability); 2. Sobolev maps between Riemannian manifolds; 3. Weak compactness and closure property; 4. Strong convergence in Sobolev spaces (definition and properties, comparison with other notions of convergence, intrinsic distance). A rich bibliography containing \(58\) suggestive references is included.