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Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited

Guy Barles·Cyril Imbert
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Abstract

The aim of this work is to revisit viscosity solutions' theory for second-order elliptic integro-differential equations and to provide a general framework which takes into account solutions with arbitrary growth at infinity. Our main contribution is a new Jensen-Ishii's Lemma for integro-differential equations, which is stated for solutions with no restriction on their growth at infinity. The proof of this result, which is of course a key ingredient to prove comparison principles, relies on a new definition of viscosity solution for integro-differential equation (equivalent to the two classical ones) which combines the approach with test-functions and sub-superjets.

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Guy Barles, Cyril Imbert. 2008-09-30. Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited. https://doi.org/10.1016/j.anihpc.2007.02.007

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