Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation

Elena Beretta; Maarten V. de Hoop; Elisa Francini; Sergio Vessella

doi:10.1080/03605302.2015.1007379

Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation

Elena Beretta, Maarten V. de Hoop, Elisa Francini, Sergio Vessella

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map. We consider piecewise constant wave speeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.

Original language	English (US)
Pages (from-to)	1365-1392
Number of pages	28
Journal	Communications in Partial Differential Equations
Volume	40
Issue number	7
DOIs	https://doi.org/10.1080/03605302.2015.1007379
State	Published - Jul 3 2015

Keywords

Helmholtz equation
Inverse boundary value problem
Lipschitz stability

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605302.2015.1007379

Cite this

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title = "Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation",

abstract = "We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map. We consider piecewise constant wave speeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.",

keywords = "Helmholtz equation, Inverse boundary value problem, Lipschitz stability",

author = "Elena Beretta and {de Hoop}, {Maarten V.} and Elisa Francini and Sergio Vessella",

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AU - Francini, Elisa

AU - Vessella, Sergio

PY - 2015/7/3

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N2 - We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map. We consider piecewise constant wave speeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.

AB - We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map. We consider piecewise constant wave speeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.

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KW - Inverse boundary value problem

KW - Lipschitz stability

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Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation

Abstract

Keywords

ASJC Scopus subject areas

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