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Zapiski Nauchnykh Seminarov LOMI, 1990, Volume 182, Pages 149–167
(Mi znsl4741)
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This article is cited in 3 scientific papers (total in 3 papers)
Investigation of a boundary value problem in a plane infinite wedge for the Laplacean with the boundary condition of a special type
V. A. Solonnikov, E. V. Frolova
Abstract:
We construct explicitly and estimate in weighted S. L. Sobolev spaces the solution of the equation $\Delta u=f$ in a plane infinite wedge satisfying the Neumann condition on one side of the wedge and the condition $\frac{\partial u}{\partial n}+h\frac{\partial u}{\partial r}+\sigma u=\psi$ on another side ($\frac\partial{\partial r}$ is the tangential derivative, $\sigma\in\mathbb{C}$, $\mathrm{Re}\,\sigma\geqslant0$). Our estimates are exact with respect to the differential order and uniform with respect to $\sigma$. The construction of the solution reduces after the Mellin transform to the investigation of a finite difference equation on the complex plane.
Citation:
V. A. Solonnikov, E. V. Frolova, “Investigation of a boundary value problem in a plane infinite wedge for the Laplacean with the boundary condition of a special type”, Boundary-value problems of mathematical physics and related problems of function theory. Part 21, Zap. Nauchn. Sem. LOMI, 182, "Nauka", Leningrad. Otdel., Leningrad, 1990, 149–167; J. Soviet Math., 62:3 (1992), 2819–2831
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https://www.mathnet.ru/eng/znsl4741 https://www.mathnet.ru/eng/znsl/v182/p149
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Abstract page: | 179 | Full-text PDF : | 55 |
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