An inverse boundary value problem for harmonic differential forms

Article type: Research Article

Authors: Joshi, M.S.^; | Lionheart, W.R.B.

Affiliations: Royal Bank of Scotland Group Risk Management, 280 Bishopsgate, London EC1M 4RB, UK E‐mail: mark_joshi@yahoo.com | Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, UK E‐mail: Bill.Lionheart@umist.ac.uk

Note: [] Corresponding author.

Abstract: We show that the full symbol of the Dirichlet to Neumann map of the k‐form Laplace's equation on a Riemannian manifold (of dimension greater than 2) with boundary determines the full Taylor series, at the boundary, of the metric. This extends the result of Lee and Uhlmann for the case k=0. The proof avoids the computation of the full symbol by using the calculus of pseudo‐differential operators parametrized by a boundary normal coordinate and recursively calculating the principal symbol of the difference of boundary operators.

Journal: Asymptotic Analysis, vol. 41, no. 2, pp. 93-106, 2005