Inverse Problems and Imaging (IPI)

Determining nonsmooth first order terms from partial boundary measurements

Pages: 349 - 369, Volume 1, Issue 2, May 2007      doi:10.3934/ipi.2007.1.349

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Kim Knudsen - Department of Mathematical Sciences, Aalborg University, Denmark (email)
Mikko Salo - Department of Mathematics and Statistics / RNI, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland (email)

Abstract: We extend results of Dos Santos Ferreira-Kenig-Sjöstrand-Uhlmann (Comm. Math. Phys., 2007) to less smooth coefficients, and we show that measurements on part of the boundary for the magnetic Schrödinger operator determine uniquely the magnetic field related to a Hölder continuous potential. We give a similar result for determining a convection term. The proofs involve Carleman estimates, a smoothing procedure, and an extension of the Nakamura-Uhlmann pseudodifferential conjugation method to logarithmic Carleman weights.

Keywords:  Inverse problem for magnetic Schrödinger operator with nonsmooth coefficients, Carleman estimate, semiclassical pseudodifferential calculus.
Mathematics Subject Classification:  35R30.

Received: September 2006;      Available Online: April 2007.