Improved estimates and a limit case for the electrostatic Klein-Gordon-Maxwell system

2009/11/30 by Antonio Azzollini, Azzollini, Antonio, Lorenzo Pisani +3
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP #msc:35J50 #msc:35J60 #msc:35Q40 #msc:35Q60

paper · pdf · doi:10.48550/arxiv.0911.5599

18 pages, a figure

arxiv created 2009/11/30 · arxiv updated 2009/12/08

Abstract

We study the class of nonlinear Klein-Gordon-Maxwell systems describing a standing wave (charged matter field) in equilibrium with a purely electrostatic field. We improve some previous existence results in the case of an homogeneous nonlinearity. Moreover, we deal with a limit case, namely when the frequency of the standing wave is equal to the mass of the charged field; this case shows analogous features of the well known "zero mass case" for scalar field equations.

Citations

• The existence of surfaces of constant mean curvature with free boundaries

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