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We consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We perform measurements of current and voltage type on a (known) part of the boundary of the conductor. We prove that, even if the defects are unknown, the current and voltage measurements at the boundary uniquely determine the corresponding electrostatic potential inside the conductor. A corresponding stability result, related to the stability of Neumann problems with respect to domain variations, is also proved. Some applications of these results to inverse problems are presented.
@article{ASNSP_2006_5_5_2_189_0,
author = {Rondi, Luca},
title = {Unique continuation from {Cauchy} data in unknown non-smooth domains},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {189--218},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 5},
number = {2},
year = {2006},
mrnumber = {2244698},
zbl = {1150.35015},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_2_189_0/}
}
TY - JOUR AU - Rondi, Luca TI - Unique continuation from Cauchy data in unknown non-smooth domains JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 189 EP - 218 VL - 5 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_2_189_0/ LA - en ID - ASNSP_2006_5_5_2_189_0 ER -
%0 Journal Article %A Rondi, Luca %T Unique continuation from Cauchy data in unknown non-smooth domains %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 189-218 %V 5 %N 2 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_2_189_0/ %G en %F ASNSP_2006_5_5_2_189_0
Rondi, Luca. Unique continuation from Cauchy data in unknown non-smooth domains. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 2, pp. 189-218. http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_2_189_0/