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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 3, Pages 518–526
(Mi smj874)
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This article is cited in 17 scientific papers (total in 17 papers)
The Carleman formula for the Helmholtz equation on the plane
È. V. Arbuzov, A. L. Bukhgeim Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We consider the Cauchy problem for the Helmholtz equation in an arbitrary bounded planar domain with Cauchy data only on part of the boundary of the domain. We derive a Carleman-type formula for a solution to this problem and give a conditional stability estimate.
Keywords:
Cauchy problem, Helmholtz equation, Carleman formula.
Received: 28.12.2004
Citation:
È. V. Arbuzov, A. L. Bukhgeim, “The Carleman formula for the Helmholtz equation on the plane”, Sibirsk. Mat. Zh., 47:3 (2006), 518–526; Siberian Math. J., 47:3 (2006), 425–432
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https://www.mathnet.ru/eng/smj874 https://www.mathnet.ru/eng/smj/v47/i3/p518
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Abstract page: | 565 | Full-text PDF : | 212 | References: | 50 |
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