Second-order elliptic integro-differential equations: viscosity solutions' theory revisited |
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Authors: | Guy Barles Cyril Imbert |
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Institution: | 1. Laboratoire de Mathématiques et Physique Théorique CNRS UMR 6083, Fédération Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours, France;2. Polytech''Montpellier & Institut de mathématiques et de modélisation de Montpellier, UMR CNRS 5149, Université Montpellier II, CC 051, Place E. Bataillon, 34 095 Montpellier cedex 5, France |
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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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Keywords: | 35D99 35J60 35B05 47G20 |
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