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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1978 Volume 78, Pages 112–127 (Mi znsl1909)

This article is cited in 7 papers

Boundary conditions on curves for the three-dimensional Laplace operator

Ya. V. Kurylev


Abstract: 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.

UDC: 517.43


 English version:
Journal of Soviet Mathematics, 1983, 22:1, 1072–1082

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