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NCTS Seminar on PDE and Analysis
 
14:20 - 15:10, May 29, 2019 (Wednesday)
R302, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 302室)
How to Obtain Parabolic Theorems from Their Elliptic Counterparts
Blair Davey (The City College of New York)

Abstract:

Experts have long realized the parallels between elliptic and parabolic theory of partial differential equations. It is well-known that elliptic theory may be considered a static, or steady-state, version of parabolic theory. And in particular, if a parabolic estimate holds, then by eliminating the time parameter, one immediately arrives at the underlying elliptic statement. Producing a parabolic statement from an elliptic statement is not as straightforward. In this talk, we demonstrate a method for producing parabolic theorems from their elliptic analogues. Specifically, we show that an Carleman estimate for the heat operator may be obtained by taking a high-dimensional limit of Carleman estimates for the Laplacian. Other applications of this technique will be discussed.



 

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