An inverse boundary value problem for harmonic differential forms

Details An inverse boundary value problem for harmonic differential forms An inverse boundary value problem for harmonic differential forms

1999-11-26

arxiv.org/abs/math/9911212v3

Asymptotic Analysis 41(2), 2005, p93-106

Mathematics

Analysis of PDEs

In this revision the assumption that the normal is known has been removed. The paper also benefits from comments at the ICMS C

Scientific paper

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.

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