Obstructions to the extension problem of Sobolev mappings

Takeshi Isobe

DOI: http://dx.doi.org/10.12775/TMNA.2003.021

Abstract


Let $M$ and $N$ be compact manifolds with $\partial M\ne\emptyset$.
We show that when $1< p< \dim M$, there are two different
obstructions to extending a map in $W^{1-1/p,p}(\partial M,N)$
to a map in $W^{1,p}(M,N)$. We
characterize one of these obstructions which is topological
in nature.
We also give properties of the other obstruction.
For some cases, we give a characterization of
$f\in W^{1-1/p,p}(\partial M,N)$ which has an
extension $F\in W^{1,p}(M,N)$.

Keywords


Sobolev mappings; extension problem; trace spaces; obstruction theory

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