國立清華大學 數學系

Abstract: The Strichartz inequality is a fundamental estimate in dispersive partial differential equations. Recently the extremal problem for this type of inequalities attracts a lot of attention starting with the work of M. Kunze for the one dimension Strichartz inequality for the Schrodinger equation. Foschi and Hundertmark-Zharnitsky independently proved that Gaussian functions are extremizers for the Strichartz inequality when the spatial dimension is one or two, and completely characterize the extremizers. In this talk, we will briefly review the background of this problem. Then based on the functional inequality of Foschi, we give an alternative proof that Gaussians are extremizers. The large part of the argument is to prove that the critical points to the Euler-Lagrange equation is complex analytic on $C^2$. This is a joint work with Jin-Cheng Jiang. Tea Time: 3:00PM, R707