Carleson measure estimates for the Green function

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Linhan Li
March 11, 2021
1:50PM - 2:50PM
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Online: Zoom info below

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Add to Calendar 2021-03-11 13:50:00 2021-03-11 14:50:00 Carleson measure estimates for the Green function Speaker:  Lihan Li (University of Minnesota) Title:  Carleson measure estimates for the Green function Speaker's URL:  https://sites.google.com/brown.edu/linhan-li/home Abstract:  Carleson measure estimates for the Green function Abstract: We are interested in the relations between an elliptic operator on a domain, the geometry of the domain, and the boundary behavior of the Green function. In a joint work with Guy David and Svitlana Mayboroda, we show that if the coefficients of the operator satisfy a quadratic Carleson condition, then the Green function on the half-space is almost affine, in the sense that the normalized difference between the Green function with a sufficiently far away pole and a suitable affine function at every scale satisfies a Carleson measure estimate. We demonstrate with counterexamples that our results are optimal, in the sense that the class of the operators considered is essentially the best possible. URL associated with Seminar https://research.math.osu.edu/pde/ Additional Dates &/or Times Zoom Link: https://osu.zoom.us/j/6146883919?pwd=M2hHVnFaMjVMb1pYT2FFZGdEVDIwdz09 Meeting ID: 6146883919 Password: 314159   Online: Zoom info below Department of Mathematics math@osu.edu America/New_York public
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Speaker:  Lihan Li (University of Minnesota)

Title:  Carleson measure estimates for the Green function

Speaker's URL:  https://sites.google.com/brown.edu/linhan-li/home

Abstract:  Carleson measure estimates for the Green function Abstract: We are interested in the relations between an elliptic operator on a domain, the geometry of the domain, and the boundary behavior of the Green function. In a joint work with Guy David and Svitlana Mayboroda, we show that if the coefficients of the operator satisfy a quadratic Carleson condition, then the Green function on the half-space is almost affine, in the sense that the normalized difference between the Green function with a sufficiently far away pole and a suitable affine function at every scale satisfies a Carleson measure estimate. We demonstrate with counterexamples that our results are optimal, in the sense that the class of the operators considered is essentially the best possible.


URL associated with Seminar
https://research.math.osu.edu/pde/

Additional Dates &/or Times
Zoom Link: https://osu.zoom.us/j/6146883919?pwd=M2hHVnFaMjVMb1pYT2FFZGdEVDIwdz09
Meeting ID: 6146883919
Password: 314159

 

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