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

Lorenzo Brasco; Erik Lindgren

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arXiv · 1508.01039

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

Lorenzo Brasco·Erik Lindgren

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Abstract

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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Lorenzo Brasco, Erik Lindgren. 2015-08-05. Higher Sobolev regularity for the fractional $p-$Laplace equation in the superquadratic case. https://arxiv.org/abs/1508.01039

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