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RECOVERY OF NON-COMPACTLY SUPPORTED COEFFICIENTS OF ELLIPTIC EQUATIONS ON AN INFINITE WAVEGUIDE

Part of: Elliptic equations and systems Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  05 November 2018

Yavar Kian
Yavar Kian*
Affiliation:
Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France (yavar.kian@univ-amu.fr)
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Abstract

We consider the unique recovery of a non-compactly supported and non-periodic perturbation of a Schrödinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of a general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different contexts including recovery of some general class of non-compactly supported coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schrödinger operator in a slab.

Keywords

inverse problemselliptic equationsscalar potentialunbounded domaininfinite cylindrical waveguideslabpartial dataCarleman estimate

MSC classification

Primary: 35R30: Inverse problems 35J15: Second-order elliptic equations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 5 , September 2020 , pp. 1573 - 1600
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Copyright
© Cambridge University Press 2018

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