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The Carleman formula for the Helmholtz equation on the plane. (Russian, English) Zbl 1115.35034

Sib. Mat. Zh. 47, No. 3, 518-526 (2006); translation in Sib. Math. J. 47, No. 3, 425-432 (2006).
Summary: 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.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35A08 Fundamental solutions to PDEs
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