Hölder regularity for nonlocal double phase equations

@article{DeFilippis2019HlderRF,
  title={H{\"o}lder regularity for nonlocal double phase equations},
  author={Cristiana De Filippis and Giampiero Palatucci},
  journal={Journal of Differential Equations},
  year={2019}
}
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 $a=a(\cdot,\cdot)$. The model case is driven by the following nonlocal double phase operator, $$ \int \!\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\, {\rm d}y + \int \!a(x,y)\frac{|u(x)-u(y)|^{q-2}(u(x)-u(y… 
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