engleski

Approximation of Green's function and application

We consider a non local boundary value problem for elliptic operator on a two dimensional domain with a small hole around origin. The precise asymptotics in terms of diameter of the hole of values of solution on boundary of the hole is described by appropriate values of the Green function associated with the origin. In case of elliptical hole it is proved that solutions converge uniformly toward the Green function associated with the origin as diameter of the ellipse tends to zero.

Green's function; asimptotics; non-local problem

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