偏微分方程讨论班
ECNU PDE Seminar

报告题目：Strauss conjecture for nontrapping obstacles
演讲人：Assist. Prof. Wang Chengbo
Johns Hopkins University
时间：2010年6月18日（星期五）下午1：30-2：30
地点：华东师大闵行校区数学系102报告厅

Abstract
In this talk, we discuss our recent work on the 2-dimensional Strauss conjecture for nontrapping obstacles. This is a joint work with H. Smith and C. Sogge.
Recently, Hidano, Metcalfe, Smith, Sogge and Zhou proved the Strauss conjecture for nontrapping obstacles when the spatial dimension n equals 3 and 4. Their method is to prove abstract Strichartz estimates, including the |x|-weighted Strichartz estimates.
In the Minkowski spacetime, the |x|-weighted Strichartz estimates (also from the work of Fang and Wang) can be utilized to prove the Strauss conjecture with n = 2, 3, 4. The reason that they can only prove the general results for n = 3, 4 is that the abstract Strichartz estimates are proved only for the case with regularity s in [(3-n)/2, (n-1)/2] (that is, s = 1/2 if n = 2). This restriction is essential for the general abstract Strichartz estimates.
In this work, we remedy this difficulty for n=2 by proving the generalized Strichartz estimates of the type L^q_t L^r_{|x|} L^2_theta. The corresponding problem for n>4 are still open.