Obstructions to the extension problem of Sobolev mappings
Keywords
Sobolev mappings, extension problem, trace spaces, obstruction theoryAbstract
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 $F\in W^{1,p}(M,N)$.Downloads
Published
2003-06-01
How to Cite
1.
ISOBE, Takeshi. Obstructions to the extension problem of Sobolev mappings. Topological Methods in Nonlinear Analysis. Online. 1 June 2003. Vol. 21, no. 2, pp. 345 - 368. [Accessed 29 March 2024].
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