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2006.388: An inverse boundary value problem for harmonic differential forms

2006.388: Mark S Joshi and William RB Lionheart (2005) An inverse boundary value problem for harmonic differential forms. Asymptotic Analysis, 41 (2). pp. 93-106. ISSN 0921-7134

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Official URL: http://iospress.metapress.com/index/WM894B89MRNQWD57.pdf

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 2000 > 35 Partial differential equations
MSC 2000 > 53 Differential geometry
MSC 2000 > 58 Global analysis, analysis on manifolds
MIMS number:2006.388
Deposited By:Prof WRB Lionheart
Deposited On:28 March 2008

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