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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:C2 - Reconstructions from Partial Boundary Data I
- Nachman\, A (Toronto)
DTSTART;TZID=Europe/London:20110725T114500
DTEND;TZID=Europe/London:20110725T123000
UID:TALK32135AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32135
DESCRIPTION:The classical inverse boundary value problem of Ca
ldern consists in determining the conductivity ins
ide a body from the Dirichlet-to-Neumann map. The
problem is of interest in medical imaging and geop
hysics\, where one seeks to image the conductivity
of a body by making voltage and current measureme
nts at its surface.\n\nBukhgeim-Uhlmann and Kenig-
Sjstrand-Uhlmann have shown that (in dimensions th
ree and higher) uniqueness in the above problem ho
lds even if measurements are available on possibly
very small subsets of the boundary. This course w
ill explain in detail a constructive proof of thes
e results\, obtained in joint work with Brian Stre
et.\n\nThe topics I hope to cover are: \n1. Review
of the reconstruction method for Caldern's proble
m with full data. \n2. New Green's functions for
the Laplacian. \n3. Boundedness properties of the
corresponding single layer operators. \n4. New s
olutions of the Schrdinger equation. \n5. Unique
solvability of the main boundary integral equation
involving only the partial Cauchy data. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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