Integrability of the Brouwer degree for irregular arguments
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 4, pp. 933-959.

We prove that the Brouwer degree deg(u,U,) for a function uC0,α(U;Rn) is in Lp(Rn) if 1p<nαd, where URn is open and bounded and d is the box dimension of ∂U. This is supplemented by a theorem showing that uju in C0,α(U;Rn) implies deg(uj,U,)deg(u,U,) in Lp(Rn) for the parameter regime 1p<nαd, while there exist convergent sequences uju in C0,α(U;Rn) such that deg(uj,U,)Lp for the opposite regime p>nαd.

DOI : 10.1016/j.anihpc.2016.07.002
Classification : 26B10, 55M25
Mots clés : Brouwer degree, Distributional Jacobian determinant, Hölder functions
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Olbermann, Heiner. Integrability of the Brouwer degree for irregular arguments. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 4, pp. 933-959. doi : 10.1016/j.anihpc.2016.07.002. http://www.numdam.org/articles/10.1016/j.anihpc.2016.07.002/

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