HAL: hal-00130169, version 3

arXiv: math/0702263

DOI: 10.1016/j.anihpc.2007.02.007

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Annales de l'Institut Henri Poincaré Analyse non linéaire 25, 3 (2008) 567-585

Available versions:

v1 (2007-02-09)

v2 (2008-09-15)

v3 (2008-09-30)

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

Guy Barles 1, Cyril Imbert 2

(2008-05-15)

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.

1:	Laboratoire de Mathématiques et Physique Théorique (LMPT)
	CNRS : UMR6083 – Université François Rabelais - Tours
2:	Institut de Mathématiques et de Modélisation de Montpellier (I3M)
	CNRS : UMR5149 – Université Montpellier II - Sciences et Techniques du Languedoc

Subject

:

Mathematics/Analysis of PDEs

Keyword(s): Integro-differential equations – Lévy operators – general nonlocal operators – stability results – Jensen-Ishii's Lemma – comparison principles – viscosity solutions – limiting semi-jets

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From: Guy Barles <>

Submitted on: Tuesday, 30 September 2008 16:11:52

Updated on: Tuesday, 30 September 2008 16:17:08