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arXiv · 1012.3183

Strichartz estimates for Dirichlet-wave equations in two dimensions with applications

Hart F. Smith·Christopher D. Sogge·Chengbo Wang
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Abstract

We establish the Strauss conjecture for nontrapping obstacles when the spatial dimension $n$ is two. As pointed out in \cite{HMSSZ} this case is more subtle than $n=3$ or 4 due to the fact that the arguments of the first two authors \cite{SmSo00}, Burq \cite{B} and Metcalfe \cite{M} showing that local Strichartz estimates for obstactles imply global ones require that the Sobolev index, $\gamma$, equal 1/2 when $n=2$. We overcome this difficulty by interpolating between energy estimates ($\gamma =0$) and ones for $\gamma=\frac12$ that are generalizations of Minkowski space estimates of Fang and the third author \cite{FaWa2}, \cite{FaWa}, the second author \cite{So08} and Sterbenz \cite{St05}.

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Hart F. Smith, Christopher D. Sogge, Chengbo Wang. 2010-12-14. Strichartz estimates for Dirichlet-wave equations in two dimensions with applications. https://doi.org/10.1090/s0002-9947-2012-05607-8

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