Sharp estimates for the wave equation via the Penrose transform

Abstract: In 2004, Foschi found the best constant, and the extremizing functions, for the Strichartz inequality for the wave equation with data in the Sobolev space $\Hdot^{1/2}\times\Hdot^{-1/2}(\R^3)$. He also formulated a conjecture, concerning the extremizers to this Strichartz inequality in all spatial dimensions $d\ge 2$. We disprove such conjecture for even $d$, but we provide evidence to support it for odd $d$. The proofs use the conformal compactification of the Minkowski space-time given by the Penrose transform.

classical analysis and ODEsfunctional analysisspectral theory

Audience: researchers in the topic

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