Global Regularity of the Reflector Problem
speaker: Jiakun Liu (Princeton University)abstract: In this talk we study a reflector system which consists of a point light source, a reflecting surface and an object to be illuminated. Due to its practical applications in optics, electro-magnetics, and acoustic, it has been extensively studied during the last half century. This problem involves a fully nonlinear partial differential equation of Monge-Ampere type, subject to a nonlinear second boundary condition. In the far field case, it is related to the reflector antenna design problem. By a duality, namely a Legendre type transform, Xu-Jia Wang has proved that it is indeed an optimal transportation problem. Therefore, the regularity results of optimal transportation can be applied. However, in the general case, the reflector problem is not an optimal transportation problem and the regularity is an extremely complicated issue. In this talk, we give necessary and sufficient conditions for the global regularity and briefly discuss their connection with the Ma-Trudinger-Wang condition in optimal transportation. This is a joint work with Neil Trudinger.
timetable:
Fri 15 Oct, 15:30 - 16:20, Aula Dini
<< Go back