American Institute of Mathematical Sciences

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May  2007, 1(2): 349-369. doi: 10.3934/ipi.2007.1.349

Determining nonsmooth first order terms from partial boundary measurements

Kim Knudsen 1, and  Mikko Salo 2,

1. 

Department of Mathematical Sciences, Aalborg University, Denmark
2. 

Department of Mathematics and Statistics / RNI, University of Helsinki, P.O. Box 68, 00014 Helsinki, Finland

Received  September 2006 Published  April 2007

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: semiclassical pseudodifferential calculus., Carleman estimate, Inverse problem for magnetic Schrödinger operator with nonsmooth coefficients.
Mathematics Subject Classification: 35R3.
Citation: Kim Knudsen, Mikko Salo. Determining nonsmooth first order terms from partial boundary measurements. Inverse Problems & Imaging, 2007, 1 (2) : 349-369. doi: 10.3934/ipi.2007.1.349
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