An inverse boundary value problem for harmonic differential forms

Joshi, Mark S and Lionheart, William RB (2005) An inverse boundary value problem for harmonic differential forms. Asymptotic Analysis, 41 (2). pp. 93-106. ISSN 0921-7134

	PDF Joshi-Lionheart-k-form-published.pdf Download (166kB)
	PDF Comments-and-Errata-Lionheart-Joshi-k-form-laplace.pdf Download (60kB)

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.

Item Type:	Article
Uncontrolled Keywords:	inverse boundary value problem, differential forms, Laplacian, Riemannian manifold, Dirichlet to Neumann map, psuedo differential operator
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 58 Global analysis, analysis on manifolds
Depositing User:	Prof WRB Lionheart
Date Deposited:	28 Mar 2008
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1046

Available Versions of this Item

• An inverse boundary value problem for harmonic differential forms. (deposited 12 Oct 2006)
  • An inverse boundary value problem for harmonic differential forms. (deposited 28 Mar 2008) [Currently Displayed]

Actions (login required)

View Item