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K-State Today

April 25, 2019

ADVANCE Distinguished Lecture Series presents Katya Krupchyk

Submitted by Tawny Ochs

The ADVANCE Distinguished Lecture Series and Lizaveta Ihnatsyeva, assistant professor of math, will host Katya Krupchyk, professor at the University of California, Irvine. Krupchyk will present "Inverse boundary problems for elliptic PDE in low regularity setting" from 2:30-3:20 p.m. Thursday, April 25, in 122 Cardwell Hall.

Krupchyk will discuss recent progress in the global uniqueness issues for inverse boundary problems for second order elliptic equations, such as the conductivity and magnetic Schrodinger equations, with low regularity coefficients. Generally speaking, in an inverse boundary problem, one wishes to determine the coefficients of a PDE inside a domain from the knowledge of its solutions along the boundary of the domain. While ubiquitous in practice, the mathematical analysis of such problems is quite challenging, and the consideration of the low regularity setting, motivated by applications, brings additional substantial difficulties. Krupchyk will discuss the case of full, as well as partial, measurements, both for domains in the Euclidean space, as well as in the more general setting of transversally anisotropic compact Riemannian manifolds with boundary. Some of the important ingredients in our approach are semiclassical Carleman estimates with limiting Carleman weights with an optimal gain of derivatives, precise smoothing estimates, as well as a construction of Gaussian beam quasimodes in a low regularity setting. This is joint work with Gunther Uhlmann.