Counter example to Strichartz estimates for the wave equation in domains

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

Let U be a bounded, regular, strictly convex domain of R^2 and consider the
wave equation on U with Dirichlet boundary condition. We prove that in such a
domain the Strichartz estimates for the wave equation suffer losses when
compared to the case U=R^2, at least for a subset of the usual range of
indices.

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