We prove that the Brouwer degree for a function is in if , where is open and bounded and d is the box dimension of ∂U. This is supplemented by a theorem showing that in implies in for the parameter regime , while there exist convergent sequences in such that for the opposite regime .
Mots clés : Brouwer degree, Distributional Jacobian determinant, Hölder functions
@article{AIHPC_2017__34_4_933_0, author = {Olbermann, Heiner}, title = {Integrability of the {Brouwer} degree for irregular arguments}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {933--959}, publisher = {Elsevier}, volume = {34}, number = {4}, year = {2017}, doi = {10.1016/j.anihpc.2016.07.002}, mrnumber = {3661865}, zbl = {1366.26018}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2016.07.002/} }
TY - JOUR AU - Olbermann, Heiner TI - Integrability of the Brouwer degree for irregular arguments JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 933 EP - 959 VL - 34 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2016.07.002/ DO - 10.1016/j.anihpc.2016.07.002 LA - en ID - AIHPC_2017__34_4_933_0 ER -
%0 Journal Article %A Olbermann, Heiner %T Integrability of the Brouwer degree for irregular arguments %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 933-959 %V 34 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2016.07.002/ %R 10.1016/j.anihpc.2016.07.002 %G en %F AIHPC_2017__34_4_933_0
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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