Arbuzov, È. V.; Bukhgeim, A. L. 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. Cited in 8 Documents MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35A08 Fundamental solutions to PDEs Keywords:Cauchy problem; Helmholtz equation; Carleman formula PDFBibTeX XMLCite \textit{È. V. Arbuzov} and \textit{A. L. Bukhgeim}, Sib. Mat. Zh. 47, No. 3, 518--526 (2006; Zbl 1115.35034); translation in Sib. Math. J. 47, No. 3, 425--432 (2006) Full Text: EuDML EMIS