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The Carleman formula for the Helmholtz equation on the plane

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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.

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Author notes

  1. A. L. Bukhgeim

    Present address: Wichita State University, USA

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    É. V. Arbuzov & A. L. Bukhgeim

Authors
  1. É. V. Arbuzov
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  2. A. L. Bukhgeim
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Additional information

Original Russian Text Copyright © 2006 Arbuzov É. V. and Bukhgeĭ A. L.

The first author was supported by the Russian Foundation for Basic Research (Grant 05-01-00250a) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-7157.2006.1); the second author was supported by NSF (Grant DMS-0505470).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 3, pp. 518–526, May–June, 2006.

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Arbuzov, É.V., Bukhgeim, A.L. The Carleman formula for the Helmholtz equation on the plane. Sib Math J 47, 425–432 (2006). https://doi.org/10.1007/s11202-006-0055-0

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  • DOI: https://doi.org/10.1007/s11202-006-0055-0

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