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Country: Finland
Abstract Title: Inverse conductivity problem with non-smooth conductivity
Abstract
In this talk we consider inverse problems for
conductivity and Schroedinger operators
in the case where conductivity or potential has co-normal
singularities in dimensions n=3,4,... For instance,
in the case where singularity is on hypersurface H, we allow
conductivity to have singularities of type dist(x,H)^{-1+a}
where a>2. The reconstruction is based on construction
of exponentially growing solutions.
Besides the uniqueness of the inverse problem, we consider
reconstruction procedures. We present a variant for the method
how the boundary values of the exponentially growing solutions
can be constructed from boundary data.
Finally, we give certain counter examples to uniqueness of inverse
problem.
The presented work has been in collaboration with
Allan Greenleaf (Univ. of Rochester) and Gunther Uhlmann (Univ. of
Washington).