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Second-order elliptic integro-differential equations: viscosity solutions’ theory revisited. (English) Zbl 1155.45004
Three types of viscosity solution of second order nonlinear elliptic integrodifferential equations are defined to account for solutions with arbitrary growth at infinity. Stability results for these viscosity solutions are derived. The Jensen-Ishii lemma is generalized and applied to prove comparison theorems.

45K05 Integro-partial differential equations
45M10 Stability theory for integral equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
45G10 Other nonlinear integral equations
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