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 Volume 42 Pagination 1510–1523 Date Published October Publisher Taylor & Francis Type of Article other ISSN 0360-5302 Abstract 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. Notes Comm. Partial Differential Equations 42 (2017), no. 10, 1510–1523. URL https://www.tandfonline.com/doi/abs/10.1080/03605302.2017.1380040 DOI 10.1080/03605302.2017.1380040
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