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+2W·∇ 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.

• NS
  National Science Foundation
• AO
  Academy of Finland
• ST
  Suomalainen Tiedeakatemia