The 2016 DiPerna Lecture was given by Gilles Lebeau (Université de Nice) on Thursday, February 18, 2016, 4PM in 60 Evans.
Strichartz Inequalities
Abstract: Strichartz inequalities first appeared, as the name correctly indicates, in a paper by Strichartz: "Restriction of Fourier Transform to Quadratic Surfaces and Decay of Solutions of Wave Equations. Duke Math. Journal, 44, 1977". They have become a fundamental tool in the study of well posedness of the Cauchy problem for nonlinear evolution equations, such as nonlinear wave or nonlinear Schrödinger equations. In harmonic analysis they are connected to Lp estimates for spectral projectors.
In this talk, we will first review some classical results on dispersive and Strichartz estimates. We will also present some new results in the case of waves inside a bounded domain (joint work with O. Ivanovici, R. Lascar and F. Planchon). Finally, we will discuss some open questions.