The Carleman formula for the Hemholtz equation on the plane
Arbuzov, E. V.
Bukhgeym, Alexander L.
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Arbuzov, É. and A. Bukhgeim (2006). "The Carleman formula for the Helmholtz equation on the plane." Siberian Mathematical Journal 47(3): 425-432.
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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Translated from Russian.