Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case.

We study the fractional p-Laplace equation (- Δ p) s u = 0 for 0 < s < 1 and in the subquadratic case 1 < p < 2 . We provide Hölder estimates with an explicit Hölder exponent. The inhomogeneous equation is also treated and there the exponent obtained is almost sharp for a certain range of parameters. Our results complement the previous results for the superquadratic case when p ≥ 2 . The arguments are based on a careful Moser-type iteration and a perturbation argument. [ABSTRACT FROM AUTHOR]