Determining nonsmooth first order terms from partial boundary measurements

2006/09/05 by Kim Knudsen, Mikko Salo, Knudsen, Kim +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Numerical methods in inverse problems #math.AP #msc:35R30

paper · pdf · doi:10.48550/arxiv.math/0609133

arxiv created 2006/09/05 · arxiv updated 2009/12/01

Abstract

We extend results of Dos Santos Ferreira-Kenig-Sjoestrand-Uhlmann (math.AP/0601466) to less smooth coefficients, and we show that measurements on part of the boundary for the magnetic Schroedinger operator determine uniquely the magnetic field related to a Hoelder 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.

Citations

• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

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