TY - JOUR
T1 - Lipschitz stable determination of polygonal conductivity inclusions in a two-dimensional layered medium from the dirichlet-to-neumann map
AU - BERETTA, ELENA
AU - FRANCINI, ELISA
AU - VESSELLA, SERGIO
N1 - Funding Information:
\ast Received by the editors September 25, 2020; accepted for publication (in revised form) April 19, 2021; published electronically August 4, 2021. https://doi.org/10.1137/20M1369609 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second and third authors was partially supported by the Research Project 201758MTR2 of the Italian Ministry of Education, University and Research (MIUR) Prin 2017 ``Direct and inverse problems for partial differential equations: theoretical aspects and applications."" \dagger Dipartimento di Matematica ``Brioschi,"" Politecnico di Milano and New York University Abu Dhabi ([email protected]). \ddagger Dipartimento di Matematica e Informatica ``U. Dini,"" Universit\à di Firenze (elisa.francini@unifi. it, [email protected]).
Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.
PY - 2021
Y1 - 2021
N2 - Using a distributed representation formula of the Gateaux derivative of the Dirichletto- Neumann map with respect to movements of a polygonal conductivity inclusion, [Beretta, et al., J. Comput. Phys., 353 (2018), pp. 264-280], we extend the results obtained in [E. Beretta and E. Francini, Appl. Anal., to appear], proving global Lipschitz stability for the determination of a polygonal conductivity inclusion, embedded in a two-dimensional layered medium, from knowledge of the Dirichlet-to-Neumann map.
AB - Using a distributed representation formula of the Gateaux derivative of the Dirichletto- Neumann map with respect to movements of a polygonal conductivity inclusion, [Beretta, et al., J. Comput. Phys., 353 (2018), pp. 264-280], we extend the results obtained in [E. Beretta and E. Francini, Appl. Anal., to appear], proving global Lipschitz stability for the determination of a polygonal conductivity inclusion, embedded in a two-dimensional layered medium, from knowledge of the Dirichlet-to-Neumann map.
KW - Conductivity equation
KW - Inverse problems
KW - Polygonal inclusions
KW - Shape derivative
KW - Stability
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U2 - 10.1137/20M1369609
DO - 10.1137/20M1369609
M3 - Article
AN - SCOPUS:85112593243
SN - 0036-1410
VL - 53
SP - 4303
EP - 4327
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 4
ER -