BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Linhan Li (University of Minnesota) DTSTART:20210517T160000Z DTEND:20210517T165000Z DTSTAMP:20260423T010139Z UID:anpdews/62 DESCRIPTION:Title: Carleson measure estimates for the Green function\nby Linhan Li (Univ ersity of Minnesota) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nWe are i nterested in the relations between an elliptic operator on a domain\, the geometry of the domain\, and the boundary behavior of the Green function. In 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 Ca rleson measure estimate. We demonstrate with counterexamples that our resu lts are optimal\, in the sense that the class of the operators considered are essentially the best possible.\n\nThis work is motivated mainly by fin ding PDE characterizations of uniform rectifiable sets with higher co-dime nsion. I’ll talk about this motivation and backgrounds\, our recent resu lts\, as well as possible directions in the future.\n LOCATION:https://researchseminars.org/talk/anpdews/62/ END:VEVENT END:VCALENDAR