Continuity of solutions to a nonlinear fractional diffusion equation

Abstract

AbstractWe study a parabolic equation for the fractional p-Laplacian of order s, for $$p\ge 2$$ p ≥ 2 and $$0<s<1$$ 0 < s < 1 . We provide space-time Hölder estimates for weak solutions, with explicit exponents. The proofs are based on iterated discrete differentiation of the equation in the spirit of Moser’s technique.