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Counterexamples to Strichartz estimates for the wave equation in domains

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Abstract

We consider the wave equation inside a strictly convex domain of dimension 2 and provide counterexamples to optimal Strichartz estimates. Such estimates inside convex domains lose regularity when compared to the flat case (at least for a subset of the usual range of indices), mainly due to microlocal phenomena such as caustics which are generated in arbitrarily small time near the boundary.

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  1. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

    Oana Ivanovici

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  1. Oana Ivanovici
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Correspondence to Oana Ivanovici.

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Ivanovici, O. Counterexamples to Strichartz estimates for the wave equation in domains. Math. Ann. 347, 627–673 (2010). https://doi.org/10.1007/s00208-009-0454-1

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