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Inverse boundary value problems at the boundary—continuous dependence
Author(s) -
Sylvester John,
Uhlmann Gunther
Publication year - 1988
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160410205
Subject(s) - mathematics , boundary value problem , boundary (topology) , current (fluid) , mathematical analysis , inverse , isotropy , conductivity , boundary values , voltage , inverse problem , geometry , physics , optics , thermodynamics , quantum mechanics
Abstract We use the methods of microlocal analysis to give a new proof of a theorem of Kohn and Vogelius, showing that the boundary values of a continuous isotropic conductivity can be recovered from voltage and current measurements at the boundary. Moreover, we prove sharp estimates to establish the continuous dependence of the boundary values of the conductivity on the voltage to current maps.