Degree and Sobolev spaces
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Degree thery, Sobolev mapsAbstrakt
Let $u$ belong (for example) to $W^{1,n+1}(S^n\times \Lambda, S^n)_{\lambda\in\Lambda}$ where $\Lambda$ is a connected open set in ${\mathbb R}^k$. For a.e. the map $x\mapsto u(x,\lambda)$ is continuous from $S^n$ into $S^n$ and therefore its (Brouwer) degree is well defined. We prove that this degree is independent of $\lambda$ a.e. in $\Lambda$. This result is extended to a more general setting, as well to fractional Sobolev spaces $W^{s,p}$ with $sp\geq n+1$.Pobrania
Opublikowane
1999-06-01
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1.
BREZIS, Haïm, LI, YanYan, MIRONESCU, Petru & NIRENBERG, Louis. Degree and Sobolev spaces. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 1999, T. 13, nr 2, s. 181–190. [udostępniono 22.7.2024].
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