LIPSCHITZ STABLE DETERMINATION OF POLYHEDRAL CONDUCTIVITY INCLUSIONS FROM LOCAL BOUNDARY MEASUREMENTS

Andrea Aspri; Elena Beretta; Elisa Francini; Sergio Vessella

doi:10.1137/22M1480550

LIPSCHITZ STABLE DETERMINATION OF POLYHEDRAL CONDUCTIVITY INCLUSIONS FROM LOCAL BOUNDARY MEASUREMENTS

Andrea Aspri, Elena Beretta, Elisa Francini, Sergio Vessella

Mathematics

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

Abstract

We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local Dirichlet-to-Neumann map extending in a highly nontrivial way the results obtained in [E. Beretta and E. Francini, Appl. Anal., 101 (2022), pp. 3536-3549] and [E. Beretta, E. Francini, and S. Vessella, SIAM J. Math. Anal., 53 (2021), pp. 4303-4327] in the two-dimensional case to the three-dimensional setting.

Original language	English (US)
Pages (from-to)	5182-5222
Number of pages	41
Journal	SIAM Journal on Mathematical Analysis
Volume	54
Issue number	5
DOIs	https://doi.org/10.1137/22M1480550
State	Published - 2022

Keywords

Lipschitz stability
conductivity inclusion
polyhedral inclusion

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/22M1480550

Cite this

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abstract = "We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local Dirichlet-to-Neumann map extending in a highly nontrivial way the results obtained in [E. Beretta and E. Francini, Appl. Anal., 101 (2022), pp. 3536-3549] and [E. Beretta, E. Francini, and S. Vessella, SIAM J. Math. Anal., 53 (2021), pp. 4303-4327] in the two-dimensional case to the three-dimensional setting.",

keywords = "Lipschitz stability, conductivity inclusion, polyhedral inclusion",

author = "Andrea Aspri and Elena Beretta and Elisa Francini and Sergio Vessella",

note = "Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",

year = "2022",

doi = "10.1137/22M1480550",

language = "English (US)",

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T1 - LIPSCHITZ STABLE DETERMINATION OF POLYHEDRAL CONDUCTIVITY INCLUSIONS FROM LOCAL BOUNDARY MEASUREMENTS

AU - Aspri, Andrea

AU - Beretta, Elena

AU - Francini, Elisa

AU - Vessella, Sergio

PY - 2022

Y1 - 2022

N2 - We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local Dirichlet-to-Neumann map extending in a highly nontrivial way the results obtained in [E. Beretta and E. Francini, Appl. Anal., 101 (2022), pp. 3536-3549] and [E. Beretta, E. Francini, and S. Vessella, SIAM J. Math. Anal., 53 (2021), pp. 4303-4327] in the two-dimensional case to the three-dimensional setting.

AB - We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local Dirichlet-to-Neumann map extending in a highly nontrivial way the results obtained in [E. Beretta and E. Francini, Appl. Anal., 101 (2022), pp. 3536-3549] and [E. Beretta, E. Francini, and S. Vessella, SIAM J. Math. Anal., 53 (2021), pp. 4303-4327] in the two-dimensional case to the three-dimensional setting.

KW - Lipschitz stability

KW - conductivity inclusion

KW - polyhedral inclusion

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LIPSCHITZ STABLE DETERMINATION OF POLYHEDRAL CONDUCTIVITY INCLUSIONS FROM LOCAL BOUNDARY MEASUREMENTS

Abstract

Keywords

ASJC Scopus subject areas

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