Obstructions to the extension problem of Sobolev mappings (Q1411266)

Let \(M\) and \(N\) be compact manifolds with \(\partial M \neq \emptyset\). In the present paper, the author shows that when \(1<p <\dim M\), then there are two different obstructions to extending a map in \(W^{1-1/p,p}(\partial M, N)\) to a map in \(W^{1,p}(M,N)\). The author characterizes one of these obstructions which is topological in nature. He also gives properties of the other obstruction. For some cases, he gives a characterization of those \(f\in W^{1-1/p,p}(\partial M,N)\) which have an extension \(F\in W^{1,p}(M,N)\).