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Nonlinear Analysis

Quantitative boundary unique continuation I

Zihui Zhao, University of Chicago

Location:  705 Hill Center
Date & time: Tuesday, 20 September 2022 at 1:40PM - 2:40PM

Abstract: Unique continuation property is a fundamental property of harmonic functions, as well as solutions to a large class of elliptic and parabolic PDEs. It says that if a harmonic function vanishes at a point to infinite order, it must vanish everywhere (in the connected set containing that point). In the same spirit, we are interested in quantitative unique continuation results, which are to use the local information about the growth rate of a harmonic function, to deduce its global properties. In this talk, I will focus on recent progress about quantitative unique continuation at the boundary. In particular, I will talk about X. Tolsa's work on the Bers problem and my joint work with C. Kenig estimating the size of the singular set of a harmonic function at the boundary.

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