Identifiability at the boundary for first-order terms
Let Ω be a domain in R n whose boundary is C 1 if n ≥3 or C 1,β if n =2. We consider a magnetic Schrödinger operator L W , q in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map
for L W , q . We also consider a steady state heat equation with convection term Δ+2 W ·∇ and recover the boundary values of the convection term W from the Dirichlet to Neumann map. Our method is constructive and gives a stability result at the boundary.
Keywords: AMS Subject Classification : 35R30; Boundary determination; Inverse problem; Magnetic Schrödinger operator
Document Type: Research Article
Affiliations: 1: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027, USA 2: Department of Mathematics and Statistics/RNI, University of Helsinki, P.O. Box 68, 00014, University of Helsinki, Finland
Publication date: 01 June 2006
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