Degree and Sobolev spaces
Keywords
Degree thery, Sobolev mapsAbstract
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 $sp\geq n+1$.Downloads
Published
1999-06-01
How to Cite
1.
BREZIS, Haïm, LI, YanYan, MIRONESCU, Petru and NIRENBERG, Louis. Degree and Sobolev spaces. Topological Methods in Nonlinear Analysis. Online. 1 June 1999. Vol. 13, no. 2, pp. 181 - 190. [Accessed 18 April 2024].
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