# Approximation of point interactions by geometric perturbations in two-dimensional domains

@article{Borisov2020ApproximationOP, title={Approximation of point interactions by geometric perturbations in two-dimensional domains}, author={Denis I. Borisov and Pavel Exner}, journal={arXiv: Mathematical Physics}, year={2020} }

We present a new type of approximation of a second-order elliptic operator in a planar domain with a point interaction. It is of a geometric nature, the approximating family consists of operators with the same symbol and regular coefficients on the domain with a small hole. At the boundary of it Robin condition is imposed with the coefficient which depends on the linear size of a hole. We show that as the hole shrinks to a point and the parameter in the boundary condition is scaled in a…

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