On Weak and Viscosity Solutions of Nonlocal Double Phase Equations

We consider the nonlocal double phase equation where 1<p\≤ q and the modulating coefficient a(\ċ, \ċ) ≥ 0. Under some suitable hypotheses, we first use the De Giorgi-Nash-Moser methods to derive the local Hölder continuity for bounded weak solutions and then establish the relationship between weak solutions and viscosity solutions to such equations.