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Abstract We study the fractional p -Laplace equation aligned (- ₚ) ˢ u = 0 aligned (- Δ p) s u = 0 for 0 0 s 1 and in the subquadratic case 1 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 p ≥ 2. The arguments are based on a careful Moser-type iteration and a perturbation argument.
Garain et al. (Fri,) studied this question.