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

Abstract

AbstractWe study the fractional p-Laplace equation $$\begin{aligned} (-\Delta _p)^s u = 0 \end{aligned}$$ ( - Δ p ) s u = 0 for $$0<s<1$$ 0 < s < 1 and in the subquadratic case $$1<p<2$$ 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 $$p\ge 2$$ p ≥ 2 . The arguments are based on a careful Moser-type iteration and a perturbation argument.