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Size estimate in a discontinuous background

Prof. Jenn-Nan Wang, National Taiwan University, Taiwan
Speaker
Prof. Jenn-Nan Wang, National Taiwan University, Taiwan
When Sep 15, 2016
from 11:00 AM to 12:00 PM
Where LH 006
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Abstract:  In this talk I would like to discuss the estimate of the size of an embedded inclusion by one boundary measurement. Here we will consider the situation where the background medium is discontinuous. A typical application of this study is to estimate the size of a cancerous tumor inside an organ by the electric impedance tomography. In this case, considering discontinuous medium is typical, for instance, the conductivities of heart, liver, intestines are 0.70 (S/m), 0.10 (S/m), 0.03 (S/m), respectively. The proof relies on quantitative uniqueness estimates for the elliptic equation with discontinuous coefficients. I plan to discuss the problem in two and three dimensions. You will see that the dimensionality affects the difficulty of the problem.

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