Accepted Paper
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Inserted: 2 aug 2015
Last Updated: 11 nov 2026

Journal: Adv. Math.
Pages: 36
Year: 2015

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 $1$.

Keywords: Fractional $p-$Laplacian, nonlocal elliptic equations, Besov regularity

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