Hölder regularity for nonlocal double phase equations

We prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two different types of fractional elliptic phases, according to the zero set of a modulating coefficient a=a(⋅,⋅). The model case is driven by the following nonlocal double phase operator,∫|u(x)−u(y)|p−2(u(x)−u(y))|x−y|n+spdy+∫a(x,y)|u(x)−u(y)|q−2(u(x)−u(y))|x−y|n+tqdy,...