Boundary conditions on curves for the three-dimensional Laplace operator

Boundary conditions on a curve for the three-dimensional Laplace operator are considered in the paper. The result is obtained in terms of a self-adjoint extension of a certain symmetric operator in $L_2(R^3)$ and leads to the following formula for the desired boundary condition: $u-\rho(\ln\rho+H(z))\dfrac{\partial u}{\partial\rho}\to0$ as $\rho\to0$ where $\rho$ is the distance to the curve, and $H(z)$ is a certain real function on this curve.