BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hui Yu (Columbia University) DTSTART:20200416T150000Z DTEND:20200416T155000Z DTSTAMP:20260423T021125Z UID:IMS/3 DESCRIPTION:Title: Regu larity of the singular set in the fully nonlinear obstacle problem\nby Hui Yu (Columbia University) as part of PDE seminar via Zoom\n\n\nAbstrac t\nObstacle problem is one of the well-studied free boundary problems. Whe n the operator is the Laplacian\, it is known that the free boundary consi sts of two parts: the regular part and the singular part. The regular part is an analytic hypersurface\, and the singular part is covered by C1-mani folds with various dimensions.\n\nWhile the tools for the study of the reg ular part is robust enough that the theory has been generalized to many ot her free boundary problems\, up to now all developments on the singular pa rt rely on monotonicity formulae. Such formulae are only expected for the Laplacian and linear operators with very regular coefficients. Consequentl y\, very little is known about the singular set when the operator is not t he Laplacian.\n\nIn this talk we describe a new method to study the singul ar set in the obstacle problem. This method does not depend on monotonicit y formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.\n\nThis is b ased on joint work with Ovidiu Savin from Columbia University.\n LOCATION:https://researchseminars.org/talk/IMS/3/ END:VEVENT END:VCALENDAR