BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Murat Akman (University of Essex) DTSTART:20210428T160000Z DTEND:20210428T165000Z DTSTAMP:20260423T010528Z UID:anpdews/60 DESCRIPTION:Title: A Minkowski-type problem for measure associated to A-harmonic PDEs\nb y Murat Akman (University of Essex) as part of HA-GMT-PDE Seminar\n\n\nAbs tract\nThe classical Minkowski problem consists in finding a convex polyhe dron from data consisting of normals to their faces and their surface area s. In the smooth case\, the corresponding problem for convex bodies is to find the convex body given the Gauss curvature of its boundary\, as a func tion of the unit normal. The proof consists of three parts: existence\, un iqueness\, and regularity. \n\n\nIn this talk\, we study a Minkowski probl em for certain measure associated with a compact convex set E with nonempt y interior and its A-harmonic capacitary function in the complement of E. Here A-harmonic PDE is a non-linear elliptic PDE whose structure is modell ed on the p-Laplace equation. If \\mu_E denotes this measure\, then the M inkowski problem we consider in this setting is that\; for a given finite Borel measure \\mu on S^(n-1)\, find necessary and sufficient conditions f or which there exists E as above with \\mu_E =\\mu. We will discuss the ex istence\, uniqueness\, and regularity of this problem in this setting.\n LOCATION:https://researchseminars.org/talk/anpdews/60/ END:VEVENT END:VCALENDAR