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
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Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00150151/en/Date
2008Journal name
Indiana University Mathematics JournalVolume
57Number
1Pages
213-246
Publication identifier
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Show full item recordAbstract (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 equationsRelated items
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