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

Imbert, Cyril; Chasseigne, Emmanuel; Barles, Guy (2008), On the Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations, Indiana University Mathematics Journal, 57, 1, p. 213-246. http://dx.doi.org/10.1512/iumj.2008.57.3315

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00150151/en/
Date
2008
Journal name
Indiana University Mathematics Journal
Volume
57
Number
1
Pages
213-246
Publication identifier
Metadata
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Author(s)
Imbert, Cyril cc
Chasseigne, Emmanuel
Barles, Guy
Abstract (EN)
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.
Subjects / Keywords
viscosity solutions; general nonlocal operators; Lévy operators; Dirichlet problem; integro-differential equations