Joshi, Mark S and Lionheart, William RB (2005) An inverse boundary value problem for harmonic differential forms. Asymptotic Analysis, 41 (2). pp. 93106. ISSN 09217134
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Abstract
We show that the full symbol of the Dirichlet to Neumann map of the kform 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 pseudodifferential 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:  http://eprints.maths.manchester.ac.uk/id/eprint/1046 
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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]
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