A sharpened Strichartz inequality for the wave equation

2018/02/12 by Giuseppe Negro, Negro, Giuseppe · 1 citation
Earth and Planetary Sciences · Mathematics · #35L05 #42B37 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1802.04114

openalex publication_date 2018/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We disprove a conjecture of Foschi, regarding extremizers for the Strichartz inequality with data in the Sobolev space H^1/2×H^-1/2(\mathbb R^d), for even d≥ 2. On the other hand, we provide evidence to support the conjecture in odd dimensions, and refine his sharp inequality in \mathbb R¹⁺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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