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

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