The Carleman formula for the Hemholtz equation on the plane

Click on the DOI link to access the article (may not be free)Translated from Russian.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.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)