We prove higher Hölder regularity for solutions of equations involving the fractional $p-$Laplacian of order $s$, when $pge 2$ and $0<1$. In particular, we provide an explicit Hölder exponent for solutions of the non-homogeneous equation with data in $L^q$ and $q>N/(sp)$, which is almost sharp whenever $sple (p−1)+N/q$. The result is new already for the homogeneous equation.
Higher Hölder regularity for the fractional p-Laplacian in the superquadratic case
Lorenzo Brasco;
2018
Abstract
We prove higher Hölder regularity for solutions of equations involving the fractional $p-$Laplacian of order $s$, when $pge 2$ and $0<1$. In particular, we provide an explicit Hölder exponent for solutions of the non-homogeneous equation with data in $L^q$ and $q>N/(sp)$, which is almost sharp whenever $sple (p−1)+N/q$. The result is new already for the homogeneous equation.File in questo prodotto:
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