# On the existence of a Feller semigroup with atomic measure in a nonlocal boundary condition

@article{Gurevich2008OnTE, title={On the existence of a Feller semigroup with atomic measure in a nonlocal boundary condition}, author={Pavel Gurevich}, journal={Proceedings of the Steklov Institute of Mathematics}, year={2008}, volume={260}, pages={157-171} }

The existence of Feller semigroups arising in the theory of multidimensional diffusion processes is studied. An elliptic operator of second order is considered on a plane bounded region G. Its domain of definition consists of continuous functions satisfying a nonlocal condition on the boundary of the region. In general, the nonlocal term is an integral of a function over the closure of the region G with respect to a nonnegative Borel measure µ(y, dη) ∈ ∂G. It is proved that the operator is a…

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