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Article Dans Une Revue Advances in Mathematics Année : 2017

Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case

Résumé

We prove that for $p\ge 2$ solutions of equations modeled by the fractional $p$-Laplacian improve their regularity on the scale of fractional Sobolev spaces. Moreover, under certain precise conditions, they are in $W^{1,p}_{loc}$ and their gradients are in a fractional Sobolev space as well. The relevant estimates are stable as the fractional order of differentiation $s$ reaches $1$.
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Dates et versions

hal-01198777 , version 1 (14-09-2015)

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Lorenzo Brasco, Erik Lindgren. Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case. Advances in Mathematics, 2017, 304, pp.300 - 354. ⟨10.1016/j.aim.2016.03.039⟩. ⟨hal-01198777⟩
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