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SUMMARY:Linhan Li (UMN)
DTSTART:20210301T220000Z
DTEND:20210301T230000Z
DTSTAMP:20260423T022815Z
UID:OARS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/15/">Ca
 rleson measure estimates for the Green function</a>\nby Linhan Li (UMN) as
  part of OARS Online Analysis Research Seminar\n\n\nAbstract\nIt is known 
 that the oscillation of the Green function for the Laplacian in a domain i
 s related to the flatness of the boundary of the domain. In a joint work w
 ith Guy David and Svitlana Mayboroda\, we consider the Green function for 
 a second-order elliptic operator in the half-space. We show that if the co
 efficients satisfy a quadratic Carleson condition\, then the Green functio
 n is almost affine\, in the sense that the normalized difference between t
 he Green function with a sufficiently far away pole and a suitable affine 
 function at every scale satisfies a Carleson measure estimate. Our results
  are optimal\, in the sense that the class of the operators considered can
 not be improved.\n\nThis work is motivated mainly by finding PDE character
 izations of uniformly rectifiable sets with higher co-dimension\, yet our 
 result is new of this kind in the co-dimension one setting as well.\n
LOCATION:https://researchseminars.org/talk/OARS/15/
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