BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Simon Bortz (University of Alabama) DTSTART:20210927T190000Z DTEND:20210927T200000Z DTSTAMP:20260423T021343Z UID:paw/33 DESCRIPTION:Title: FKP meets DKP\nby Simon Bortz (University of Alabama) as part of Probabil ity and Analysis Webinar\n\n\nAbstract\nIn the 80’s Dahlberg asked two q uestions regarding the `$L^p$ – solvability’ of elliptic equations wit h variable coefficients. Dahlberg’s first question was whether $L^p$ sol vability was maintained under `Carleson-perturbations’ of the coefficien ts. This question was answered by Fefferman\, Kenig and Pipher [FKP]\, whe re they also introduced new characterizations of $A_\\infty$\, reverse-Hö lder and $A_p$ weights. These characterizations were used to create a coun terexample to show their theorem was sharp.\n \nDahlberg’s second questi on was whether a Carleson gradient/oscillation condition (the `DKP conditi on’) was enough to imply $L^p$ solvability for some p > 1. This was answ ered by Kenig and Pipher [KP] and refined by Dindos\, Petermichl and Piphe r [DPP] (in the `small constant’ case). These $L^p$ solvability results can be interpreted in terms of a reverse Hölder condition for the ellipt ic kernel and therefore connected with the $A_\\infty$ condition. In this talk\, we discuss L^p solvability for a class of coefficients that satisfi es a `weak DKP condition’. In particular\, we connect the (weak) DKP con dition to the characterization of $A_\\infty$ in [FKP]. This allows us to treat the `large’\, `small’ and ‘vanishing’ (weak) DKP conditions simultaneously and independently from the works [KP] and [DPP]. \n \nThis is joint work with my co-authors Egert\, Saari\, Toro and Zhao. A proof of the main estimate will be sketched\, but technical details will be avoide d.\n LOCATION:https://researchseminars.org/talk/paw/33/ END:VEVENT END:VCALENDAR