Publication: Fractional Sobolev regularity for the Brouwer degree
Fractional Sobolev regularity for the Brouwer degree
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De Lellis, C., & Inauen, D. (2017). Fractional Sobolev regularity for the Brouwer degree. Communications in Partial Differential Equations, 42(10), 1510–1523. https://doi.org/10.1080/03605302.2017.1380040
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Abstract
We prove that if Ω⊂ℝn is a bounded open set and nα>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 β≥0 and p≥1 with there is a vector field with deg (v,Ω,⋅)∉Wβ,p, where is the unit ball.
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- De Lellis, Camillo
- Inauen, Dominik
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De Lellis, C., & Inauen, D. (2017). Fractional Sobolev regularity for the Brouwer degree. Communications in Partial Differential Equations, 42(10), 1510–1523. https://doi.org/10.1080/03605302.2017.1380040
