To the theory of Sobolev-type classes of functions with values in a metric space

We study some classes of functions with values in a complete metric space which can be considered as analogs of the Sobolev spaces $W_p^1$ . Earlier the author considered the case of functions on a domain of $\mathbb{R}^n$. Here we study the general case of mappings on an arbitrary Lipschitz manifold. We give necessary auxiliary facts, consider some examples, and describe some methods of construction of lower semicontinuous functionals on the classes $W_p^1(M)$, where $M$ is a Lipschitz manifold.