Integrability of the Brouwer degree for irregular arguments
(2017) Annales de l’Institut Henri Poincaré - C - Non Linear Analysis — Vol. 34, n° 4, p. 933-959 (2017)
Files
integrabilityofthebrouwerdegree.pdf
Open Access - Adobe PDF
- 349.29 KB
Details
- Authors
- Abstract
- We prove that the Brouwer degree deg(u,U,⋅) for a function u∈C0,α(U;ℝn) is in Lp(ℝn) if 1≤p<nαd, where U⊂ℝn is open and bounded and d is the box dimension of ∂U. This is supplemented by a theorem showing that uj→u in C0,α(U;ℝn) implies deg(uj,U,⋅)→deg(u,U,⋅) in Lp(ℝn) for the parameter regime 1≤p<nαd, while there exist convergent sequences uj→u in C0,α(U;ℝn) such that ‖deg(uj,U,⋅)‖Lp→∞ for the opposite regime p>nαd.
- Affiliations
Universität Bonn
Citations
Olbermann, H. (2017). Integrability of the Brouwer degree for irregular arguments. Annales de l’Institut Henri Poincaré - C - Non Linear Analysis, 34(4), 933-959. https://doi.org/10.1016/j.anihpc.2016.07.002 (Original work published 2017)