|Title||Fractional Sobolev regularity for the Brouwer degree|
|Publication Type||Journal Article|
|Year of Publication||2017|
|Authors||De Lellis C., Inauen D.|
|Journal||Communications in Partial Differential Equations|
|Publisher||Taylor & Francis|
|Type of Article||other|
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.