Geodesic
Boundary conditions on curves for the three-dimensional Laplace operator
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 112-127

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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. 
@article{ZNSL_1978_78_a7,
     author = {Ya. V. Kurylev},
     title = {Boundary conditions on curves for the three-dimensional {Laplace} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {112--127},
     publisher = {mathdoc},
     volume = {78},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a7/}
}
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Ya. V. Kurylev. Boundary conditions on curves for the three-dimensional Laplace operator. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 112-127. http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a7/