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SUMMARY:C2 - Reconstructions from Partial Boundary Data II - Nachman\, A (
 Toronto)
DTSTART:20110725T141500Z
DTEND:20110725T150000Z
UID:TALK32134@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The classical inverse boundary value problem of Caldern consis
 ts in determining the conductivity inside a body from the Dirichlet-to-Neu
 mann map. The problem is of interest in medical imaging and geophysics\, w
 here one seeks to image the conductivity of a body by making voltage and c
 urrent measurements at its surface.\n\nBukhgeim-Uhlmann and Kenig-Sjstrand
 -Uhlmann have shown that (in dimensions three and higher) uniqueness in th
 e above problem holds even if measurements are available on possibly very 
 small subsets of the boundary. This course will explain in detail a constr
 uctive proof of these results\, obtained in joint work with Brian Street.\
 n\nThe topics I hope to cover are: \n1. Review of the reconstruction metho
 d for Caldern's problem with full data.  \n2. New Green's functions for th
 e Laplacian.  \n3. Boundedness properties of the corresponding single laye
 r operators.  \n4. New solutions of the Schrdinger equation.  \n5. Unique 
 solvability of the main boundary integral equation involving only the part
 ial Cauchy data.  \n
LOCATION:Seminar Room 1\, Newton Institute
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