Strichartz estimates for Dirichlet-wave equations in two dimensions with applications
| Autor: | Chengbo Wang, Christopher D. Sogge, Hart F. Smith |
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| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
Conjecture Applied Mathematics General Mathematics Dimension (graph theory) Mathematics::Analysis of PDEs Wave equation 35L71 Dirichlet distribution Sobolev space symbols.namesake Mathematics - Analysis of PDEs Minkowski space FOS: Mathematics symbols Energy (signal processing) Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | ResearcherID |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | 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}. Comment: Final version, to appear in the Transactions of the AMS. 20 pages, 2 figures |
| Databáze: | OpenAIRE |
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