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

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

2010-12-14

arxiv.org/abs/1012.3183v2

Transactions of the American Mathematical Society, 364 (2012), 3329-3347

Mathematics

Analysis of PDEs

Final version, to appear in the Transactions of the AMS. 20 pages, 2 figures

Scientific paper

10.1090/S0002-9947-2012-05607-8

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}.

Affiliated with

Also associated with

No associations

Rating

Strichartz estimates for Dirichlet-wave equations in two dimensions with applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Strichartz estimates for Dirichlet-wave equations in two dimensions with applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Strichartz estimates for Dirichlet-wave equations in two dimensions with applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-13007