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arXiv · 1904.12549

An estimate of the Hopf degree of fractional Sobolev mappings

Armin Schikorra·Jean Van Schaftingen
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Abstract

We estimate the Hopf degree for smooth maps $f$ from $\mathbb{S}^{4n-1}$ to $\mathbb{S}^{2n}$ in the fractional Sobolev space. Namely we show that for $s \in [1 - \frac{1}{4n}, 1]$ \[ \left |{\rm deg}_H(f)\right | \lesssim [f]_{W^{s,\frac{4n-1}{s}}}^{\frac{4n}{s}}. \] Our argument is based on the Whitehead integral formula and commutator estimates for Jacobian-type expressions.

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Armin Schikorra, Jean Van Schaftingen. 2019-04-29. An estimate of the Hopf degree of fractional Sobolev mappings. https://doi.org/10.1090/proc%2F15026

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