LOCAL UNIQUENESS IN THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT

Authors
ALESSANDRINI G ISAKOV V POWELL J
Citation
G. Alessandrini et al., LOCAL UNIQUENESS IN THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT, Transactions of the American Mathematical Society, 347(8), 1995, pp. 3031-3041
Citations number
14
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
347
Issue
8
Year of publication
1995
Pages
3031 - 3041
Database
ISI
SICI code
0002-9947(1995)347:8<3031:LUITIC>2.0.ZU;2-8
Abstract
We prove local uniqueness of a domain D entering the conductivity equa tion div((1 + chi(D))del u) = 0 in a bounded planar domain Omega given the Cauchy data for u on a part of partial derivative Omega. The main assumption is that del u has zero index on partial derivative Omega w hich is easy to guarantee by choosing special boundary data for u. To achieve our goals we study index of critical points of u on partial de rivative Omega.