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APRG Seminar

Title: Carleman Estimates and Unique Continuation
Speaker: Ramesh Manna (IISc Mathematics)
Date: 14 October 2020
Time: 4 pm
Venue: Microsoft Teams (online)

In this talk, we discuss Carleman estimates for Laplacian, which implies strong unique continuation for $-\Delta u+Vu$ with potential $V \in L^{\infty}.$ We briefly discuss unique continuation in certain critical situations such as when the potential is in $L^{n/2}_{loc}$ assuming Fourier restriction theorems. Then $L^{n/2}_{loc}$ case is a well-known result of Kenig-Jerison. Our proof of unique continuation is based on the Carleman estimate where it is a consequence of the spectral gap of Laplace Beltrami on the sphere.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 15 Jul 2024