An estimate of the Hopf degree of fractional Sobolev mappings
(2020) Proceedings of the American Mathematical Society — Vol. 148, n° 7, p. 2877-2891 (2020)
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- Abstract
- We estimate the Hopf degree for smooth maps f from S^4n−1 to S^2n in the fractional Sobolev space. Namely we show that for s∈[1−1/(4n),1], |deg_H(f)|≲[f]^4ns_W^s,4n−1/s. Our argument is based on the Whitehead integral formula and commutator estimates for Jacobian-type expressions.
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Schikorra, A., & Van Schaftingen, J. (2020). An estimate of the Hopf degree of fractional Sobolev mappings. Proceedings of the American Mathematical Society, 148(7), 2877-2891. https://doi.org/10.1090/proc/15026 (Original work published 2020)