Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The Neumann problem for the equation $ \Delta u - k^2u=0$ in the exterior of non-closed Lipschitz surfaces


Author: P. A. Krutitskii
Journal: Quart. Appl. Math. 72 (2014), 85-91
MSC (2010): Primary 35J05, 35J25, 31A10, 31A25
DOI: https://doi.org/10.1090/S0033-569X-2013-01319-4
Published electronically: November 13, 2013
MathSciNet review: 3185133
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Abstract: We study the Neumann problem for the equation $ \Delta u - k^2u=0$ in the exterior of non-closed Lipschitz surfaces in $ R^3$. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of a double layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.


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Additional Information

P. A. Krutitskii
Affiliation: KIAM, Miusskaya Sq. 4, Moscow, 125047, Russia
Email: biem@mail.ru

DOI: https://doi.org/10.1090/S0033-569X-2013-01319-4
Received by editor(s): February 26, 2012
Published electronically: November 13, 2013
Article copyright: © Copyright 2013 Brown University


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