Integrability of the Brouwer degree for irregular arguments

  • Heiner Olbermann

    Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Abstract

We prove that the Brouwer degree for a function is in if , where is open and bounded and is the box dimension of . 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 .

Cite this article

Heiner Olbermann, Integrability of the Brouwer degree for irregular arguments. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 4, pp. 933–959

DOI 10.1016/J.ANIHPC.2016.07.002