Local boundedness and Hölder continuity for the parabolic fractional p-Laplace equations.

In this paper, we study the boundedness and Hölder continuity of local weak solutions to the following nonhomogeneous equation ∂ t u (x , t) + P. V. ∫ R N K (x , y , t) | u (x , t) - u (y , t) | p - 2 (u (x , t) - u (y , t)) d y = f (x , t , u) <graphic href="526_2020_1870_Article_Equ165.gif"></graphic> in Q T = Ω × (0 , T) , where the symmetric kernel K(x, y, t) has a generalized form of the fractional p-Laplace operator of s-order. We impose some structural conditions on the function f and use the De Giorgi-Nash-Moser iteration to establish the boundedness of local weak solutions in the a priori way. Based on the boundedness result, we also obtain Hölder continuity of bounded solutions in the superquadratic case. These results can be regarded as a counterpart to the elliptic case due to Di Castro et al. (Ann Inst H Poincaré Anal Non Linéaire, 2016). [ABSTRACT FROM AUTHOR]