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:20260404T143403Z UID:IMS/3 DESCRIPTION:Title: Regularity of the singular set in the fully nonlinear obstacle problem< /a>\nby Hui Yu (Columbia University) as part of PDE seminar via Zoom\n\n\n Abstract\nObstacle problem is one of the well-studied free boundary proble ms. When the operator is the Laplacian\, it is known that the free boundar y consists of two parts: the regular part and the singular part. The regul ar part is an analytic hypersurface\, and the singular part is covered by C1-manifolds with various dimensions.\n\nWhile the tools for the study of the regular part is robust enough that the theory has been generalized to many other free boundary problems\, up to now all developments on the sing ular part rely on monotonicity formulae. Such formulae are only expected f or the Laplacian and linear operators with very regular coefficients. Cons equently\, very little is known about the singular set when the operator i s not the Laplacian.\n\nIn this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on mono tonicity formulae and works for fully nonlinear elliptic operators. The re sult we get matches the best-known result for the case of Laplacian.\n\nTh is is based on joint work with Ovidiu Savin from Columbia University.\n LOCATION:https://stable.researchseminars.org/talk/IMS/3/ END:VEVENT END:VCALENDAR