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
This is the latest version of this eprint.
Full text available as:
|PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
|PDF (Comments and errata) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader|
Official URL: http://iospress.metapress.com/index/WM894B89MRNQWD57.pdf
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.
|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
|Deposited By:||Prof WRB Lionheart|
|Deposited On:||28 March 2008|
Available Versions of this Item
- An inverse boundary value problem for harmonic differential forms (deposited 28 March 2008) [Currently Displayed]