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Pré-Publication, Document De Travail Année : 2007

On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations

Résumé

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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Dates et versions

hal-00150151 , version 1 (29-05-2007)
hal-00150151 , version 2 (27-09-2007)
hal-00150151 , version 3 (15-02-2008)

Identifiants

  • HAL Id : hal-00150151 , version 2

Citer

Guy Barles, Emmanuel Chasseigne, Cyril Imbert. On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations. 2007. ⟨hal-00150151v2⟩
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