We prove that if ??$R$n is a bounded open set and n\ensuremathα\ensuremath>dimb(??) = d, then the Brouwer degree deg(v,?,$\cdot$) of any Hölder function belongs to the Sobolev space for every . This extends a summability result of Olbermann and in fact we get, as a byproduct, a more elementary proof of it. Moreover, we show the optimality of the range of exponents in the following sense: for every \ensuremathβ?0 and p?1 with there is a vector field with deg (v,?,$\cdot$)?W\ensuremathβ,p, where is the unit ball.

Comm. Partial Differential Equations 42 (2017), no. 10, 1510–1523.