STRICHARTZ ESTIMATES FOR DIRICHLET-WAVE EQUATIONS IN TWO DIMENSIONS WITH APPLICATIONS

被引：36

作者：

Smith, Hart F. ^{[1
]}

Sogge, Christopher D. ^{[2
]}

Wang, Chengbo ^{[2
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Johns Hopkins Univ, Dept Math, Baltimore, MD 21218 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 364卷 / 06期

关键词：

Strichartz estimates; Strauss conjecture; obstacles; STRAUSS-CONJECTURE; EXISTENCE;

D O I：

10.1090/S0002-9947-2012-05607-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the Strauss conjecture for nontrapping obstacles when the spatial dimension n is two. As pointed out by Hidano, Metcalfe, Smith, Sogge, and Zhou (2010) this case is more subtle than n = 3 or 4 due to the fact that the arguments in the papers of the first two authors (2000), Burg (2000) and Metcalfe (2004), showing that local Strichartz estimates for obstacles imply global ones, require that the Sobolev index, gamma, equals 1/2 when n = 2. We overcome this difficulty by interpolating between energy estimates (gamma = 0) and ones for gamma = 1/2 that are generalizations of Minkowski space estimates of Fang and the third author (2006), (2011), the second author (2008) and Sterbenz (2005).

引用

收藏

页码：3329 / 3347

页数：19

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