È. V. Arbuzov, A. L. Bukhgeim, “The Carleman formula for the Maxwell’s equations on a plane”, Sib. Èlektron. Mat. Izv., 2008, Volume 5,Pages <nobr>448

This article is cited in 2 papers

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The Carleman formula for the Maxwell’s equations on a plane

È. V. Arbuzov^a, A. L. Bukhgeim^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Wichita State University, Department of Mathematics and Statiatics

Abstract: We consider the Cauchy problem for second-order elliptic equations in an arbitrary bounded planar domain with Cauchy data only on a 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. Then the result is applied to Maxwell's system.

Keywords: Cauchy problem, second-order elliptic equations, Carleman formula, Maxwell's system.

UDC: 517.55

MSC: 35J25

Received July 1, 2008, published November 24, 2008