Best constant of 3D Anisotropic Sobolev inequality and its applications

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May 2010, 9(3): 655-666. doi: 10.3934/cpaa.2010.9.655

Best constant of 3D Anisotropic Sobolev inequality and its applications

1.	School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

Received June 2009 Revised October 2009 Published January 2010

Abstract
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In this paper, we firstly determine the best constant of the three dimensional anisotropic Sobolev inequality [2]; then we use this best constant to investigate qualitative conditions for the uniform bound of the solution of the generalized Kadomtsev-Petviashvili (KP) I equation in three dimensions. The (KP) I equation is a model for the propagation of weakly nonlinear dispersive long waves on the surface of a fluid, when the wave motion is essentially one- directional and weak transverse effects are taken into account [11, 10]. Our results improve and optimize previous works [6, 12, 13, 14, 15].

Keywords: uniform bound of the solution., Best constant of the anisotropic Sobolev inequality, Kadomtsev- Petviashvili equation.

Mathematics Subject Classification: Primary: 35B40; Secondary: 35J2.

Citation: Jianqing Chen. Best constant of 3D Anisotropic Sobolev inequality and its applications. Communications on Pure & Applied Analysis, 2010, 9 (3) : 655-666. doi: 10.3934/cpaa.2010.9.655

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