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NCTS Seminar on PDE and Analysis
 
14:20 - 15:20, January 5, 2017 (Thursday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Recent Progress on Landis’ Conjecture
Blair Davey (The City College of New York)

Abstract 

In the late 1960s, E.M. Landis made the following conjecture: 

If and are bounded functions, and is a solution to in that decays like , then must be identically zero. In 1992, V. Z. Meshkov disproved this conjecture by constructing bounded functions \Delta u = V u and satisfy .
The result of Meshkov was accompanied by qualitative unique continuation estimates for solutions in . In 2005, J. Bourgain and C. Kenig quantified Meshkov's unique continuation estimates.These results, and the generalizations that followed, have led to a fairly complete understanding of the complex-valued setting.However, there are reasons to believe that Landis' conjecture may be true in the real-valued setting.We will discuss recent progress towards resolving the real-valued version of Landis' conjecture in the plane.


 

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