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| HAL: hal-00150151, version 3 |
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| Indiana University Mathematics Journal 57, 1 (2008) 213-146 |
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| Available versions: | v1 (2007-05-29) | v2 (2007-09-27) | v3 (2008-02-15) |
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| On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations |
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| Guy Barles 1Emmanuel Chasseigne 1 |
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| (2008) |
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| In this article, we consider the analogue of the Dirichlet problem for second-order elliptic integro-differential equations, which consists in imposing the "boundary conditions" in the whole complementary of the domain. We are looking for conditions on the differential and integral parts of the equation in order to ensure that the Dirichlet boundary condition is satisfied in the classical sense or, in other words, in order that the solution agrees with the Dirichlet data on the boundary of the domain. We also provide a general existence result of a continuous viscosity solution of the nonlocal Dirichlet problem by using Perron's method. |
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| 1: | Laboratoire de Mathématiques et Physique Théorique (LMPT) |
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CNRS : UMR6083 – Université François Rabelais - Tours |
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| 2: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| Subject | : | Mathematics/Analysis of PDEs |
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| integro-differential equations – Dirichlet problem – Lévy operators – general nonlocal operators – viscosity solutions |
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| hal-00150151, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00150151 | |
| oai:hal.archives-ouvertes.fr:hal-00150151 | |
| From: Cyril Imbert | |
| Submitted on: Friday, 15 February 2008 09:29:29 | |
| Updated on: Wednesday, 11 February 2009 06:33:31 | |
