Obstructions to the extension problem of Sobolev mappings
Słowa kluczowe
Sobolev mappings, extension problem, trace spaces, obstruction theoryAbstrakt
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 $F\in W^{1,p}(M,N)$.Pobrania
Opublikowane
2003-06-01
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1.
ISOBE, Takeshi. Obstructions to the extension problem of Sobolev mappings. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2003, T. 21, nr 2, s. 345–368. [udostępniono 22.7.2024].
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