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Low regularity function spaces of $N$-valued maps are contractible

Petru Mironescu

Abstract


Let $M$ be a compact Lipschitz submanifold, possibly with boundary, of $\mathbb{R} ^n$. Let $N\subset \mathbb{R} ^k$ be an arbitrary set. Let $s\ge 0$ and $1\le p<\infty $ be such that $sp<1$. Then $W^{s, p}(M ; N)$ is contractible.


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References


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DOI: http://dx.doi.org/10.7146/math.scand.a-26360

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