We consider the problem of determining a polyhedral conductivity inclusion embed-ded 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.
LIPSCHITZ STABLE DETERMINATION OF POLYHEDRAL CONDUCTIVITY INCLUSIONS FROM LOCAL BOUNDARY MEASUREMENTS / A. Aspri, E. Beretta, E. Francini, S. Vessella. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 54:5(2022), pp. 5182-5222. [10.1137/22M1480550]
LIPSCHITZ STABLE DETERMINATION OF POLYHEDRAL CONDUCTIVITY INCLUSIONS FROM LOCAL BOUNDARY MEASUREMENTS
A. AspriPrimo
Writing – Review & Editing
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2022
Abstract
We consider the problem of determining a polyhedral conductivity inclusion embed-ded 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.
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