A perturbative approach to Hölder continuity of solutions to a nonlocal p-parabolic equation

Abstract

AbstractWe study local boundedness and Hölder continuity of a parabolic equation involving the fractional p-Laplacian of order s, with $$0<s<1$$ 0 < s < 1 , $$2\le p < \infty $$ 2 ≤ p < ∞ , with a general right-hand side. We focus on obtaining precise Hölder continuity estimates. The proof is based on a perturbative argument using the already known Hölder continuity estimate for solutions to the equation with zero right-hand side.