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

We study the fractional p-Laplace equation (Formula presented.) 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.