A sharpened energy-Strichartz inequality for the wave equation

TL;DR

This paper refines the sharp Strichartz estimate for the wave equation in 5+1 dimensions by adding a term that measures the distance from the set of maximizers, enhancing understanding of extremal functions.

Contribution

It introduces a sharpened version of the energy-Strichartz inequality for the wave equation, incorporating a distance-based correction term to improve the classical estimate.

Findings

Refinement of the sharp Strichartz estimate for wave equations in 5+1 dimensions

Introduction of a distance-based correction term to the inequality

Enhanced characterization of extremizers for the inequality

Abstract

We consider the sharp Strichartz estimate for the wave equation on $\mathbb R^{1+5}$ in the energy space, due to Bez and Rogers. We show that it can be refined by adding a term proportional to the distance from the set of maximisers, in the spirit of the classical sharpened Sobolev estimate of Bianchi and Egnell.