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

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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Submitted on : Tuesday, September 30, 2008 - 4:11:52 PM
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Guy Barles, Cyril Imbert. Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2008, 25 (3), pp.567-585. ⟨10.1016/j.anihpc.2007.02.007⟩. ⟨hal-00130169v3⟩

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