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Fractional Sobolev regularity for the Brouwer degree
2017
Communications in Partial Differential Equations
We prove that if Ωn is a bounded open set and n>dimb(Ω) = d, then the Brouwer degree deg(v,Ω,) 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 0 and p1 with there is a vector field with deg (v,Ω,)W,p, where is the unit ball. Abstract. We prove that if Ω ⊂ R n is a bounded
doi:10.1080/03605302.2017.1380040
fatcat:uifgtoqisjhnnns2mmxrp4hq4a