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

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1365-1392
Number of pages28
JournalCommunications in Partial Differential Equations
Volume40
Issue number7
DOIs
StatePublished - Jul 3 2015

Fingerprint

Helmholtz equation
Helmholtz Equation
Boundary value problems
Partition
Lipschitz Stability
Inverse Boundary Value Problem
Dirichlet-to-Neumann Map
Hausdorff Distance
Stability Estimates
Wave Speed
Unknown

Keywords

  • Helmholtz equation
  • Inverse boundary value problem
  • Lipschitz stability

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation. / Beretta, Elena; de Hoop, Maarten V.; Francini, Elisa; Vessella, Sergio.

In: Communications in Partial Differential Equations, Vol. 40, No. 7, 03.07.2015, p. 1365-1392.

Research output: Contribution to journalArticle

Beretta, Elena ; de Hoop, Maarten V. ; Francini, Elisa ; Vessella, Sergio. / Stable Determination of Polyhedral Interfaces from Boundary Data for the Helmholtz Equation. In: Communications in Partial Differential Equations. 2015 ; Vol. 40, No. 7. pp. 1365-1392.
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