Unique continuation from Cauchy data in unknown non-smooth domains

Luca Rondi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 2, page 189-218
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Rondi, Luca. "Unique continuation from Cauchy data in unknown non-smooth domains." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.2 (2006): 189-218. <http://eudml.org/doc/242331>.

@article{Rondi2006,
abstract = {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.},
author = {Rondi, Luca},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Neumann problem; inverse boundary value problem; stability; ill-posed problem; continuation; harmonic analysis},
language = {eng},
number = {2},
pages = {189-218},
publisher = {Scuola Normale Superiore, Pisa},
title = {Unique continuation from Cauchy data in unknown non-smooth domains},
url = {http://eudml.org/doc/242331},
volume = {5},
year = {2006},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 2
SP - 189
EP - 218
AB - 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.
LA - eng
KW - Neumann problem; inverse boundary value problem; stability; ill-posed problem; continuation; harmonic analysis
UR - http://eudml.org/doc/242331
ER -

References

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