Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy

We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at least one viscosity solution of class C l o c 1 , α , for some constant α ∈ ( 0 , 1 ) . In addition, under suitable conditions on degree of the operator σ , we prove regularity estimates in Hölder spaces for any viscosity solution. We also examine the singular setting and prove Hölder regularity estimates for the gradient of the solutions.