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May 7, 2022 at 6:28 vote accept Luis Yanka Annalisc
May 6, 2022 at 13:10 comment added Willie Wong @PedroLauridsenRibeiro Thanks for the addition! I have not looked deeply at that case so my knowledge of the literature is definitely spotty. My answer above is intended to give the OP some places to start looking, and is absolutely not meant to be exhaustive.
May 6, 2022 at 2:00 comment added Pedro Lauridsen Ribeiro I believe the 1993 JAMS paper by Mockenhaupt, Seeger and Sogge was the first to establish the (space-time) local Strichartz estimates for varying-coefficient wave and Klein-Gordon equations in full generality. These are also discussed in the last chapter of the book "Fourier Integrals in Classical Analysis" by the last author.
May 6, 2022 at 1:52 history answered Willie Wong CC BY-SA 4.0