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arXiv · 1802.04114

A sharpened Strichartz inequality for the wave equation

Giuseppe Negro
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Abstract

We disprove a conjecture of Foschi, regarding extremizers for the Strichartz inequality with data in the Sobolev space $\dot{H}^{1/2}\times\dot{H}^{-1/2}(\mathbb R^d)$, for even $d\ge 2$. On the other hand, we provide evidence to support the conjecture in odd dimensions, and refine his sharp inequality in $\mathbb R^{1+3}$, adding a term proportional to the distance of the initial data from the set of extremizers. The proofs use the conformal compactification of the Minkowski space-time given by the Penrose transform.

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Giuseppe Negro. 2018-02-12. A sharpened Strichartz inequality for the wave equation. https://arxiv.org/abs/1802.04114

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