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Published in:
Inverse Problems Read chapter Read first chapter

2017 | OriginalPaper | Chapter

5. Elliptic Equations: Many Boundary Measurements

Author : Victor Isakov

Published in: Inverse Problems for Partial Differential Equations

Publisher: Springer International Publishing

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Abstract

We consider the Dirichlet problem (4.0.1), (4.0.2). At first we assume that for any Dirichlet data g 0 we are given the Neumann data g 1; in other words, we know the results of all possible boundary measurements, or the so-called Dirichlet-to-Neumann operator \(\mathrm{\Lambda }: H^{1/2}(\partial \Omega ) \rightarrow H^{-1/2}(\partial \Omega )\), which maps the Dirichlet data g 0 into the Neumann data g 1.

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previous chapter Elliptic Equations: Single Boundary Measurements
next chapter Scattering Problems and Stationary Waves
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Metadata
Title
Elliptic Equations: Many Boundary Measurements
Author
Victor Isakov
Copyright Year
2017
Book
Inverse Problems for Partial Differential Equations

Print ISBN: 978-3-319-51657-8

Electronic ISBN: 978-3-319-51658-5

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-51658-5_5

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