58 research outputs found

    On extremizing sequences for the adjoint restriction inequality on the cone

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    It is known that extremizers for the L2L^2 to L6L^6 adjoint Fourier restriction inequality on the cone in R3\mathbb{R}^3 exist. Here we show that nonnegative extremizing sequences are precompact, after the application of symmetries of the cone. If we use the knowledge of the exact form of the extremizers, as found by Carneiro, then we can show that nonnegative extremizing sequences converge, after the application of symmetries.Comment: 27 pages. Includes referee comment

    Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

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    We study the problem of existence of extremizers for the L2L^2 to LpL^p adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases pp is an even integer. We will use the method developed by Foschi to show that extremizers do not exist.Comment: 32 pages. Correction for Theorem 1.2 and Proposition 7.5 and addition of Remark 1.
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