We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.
Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation / Elena Beretta; Maarten V. de Hoop; Elisa Francini; Sergio Vessella. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 40:(2015), pp. 1365-1392. [10.1080/03605302.2015.1007379]
Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation
FRANCINI, ELISA;VESSELLA, SERGIO
2015
Abstract
We study an inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map as the data. We consider piecewise constant wavespeeds on an unknown tetrahedral partition and prove a Lipschitz stability estimate in terms of the Hausdorff distance between partitions.
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