Local smoothing for the wave equation in 2+1 dimensions

Abstract: Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in R^{2+1}. I will talk about our proof and explain several important ingredients such as induction on scales and an incidence type theorem.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom