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Regularity results for nonlocal equations by approximation. (English) Zbl 1231.35284
This paper is concerned with existence and regularity results for nonlocal elliptic equations which include applications in stochastic control problems and stochastic games. By using compactness and perturbative methods and previous results for the translation-invariant case, the authors obtain Cordes-Nirenberg type (\(C^{1,\alpha}\)) estimates for nonlocal elliptic equations that are not necessarily translation-invariant. Applications of the abstract theorem are provided in the paper, which include linear and nonlinear equations with variable coefficients and nonlinear equations with constant coefficients but non-differentiable kernels.

MSC:
35R09 Integral partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
35D40 Viscosity solutions to PDEs
91A15 Stochastic games, stochastic differential games
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