Solitary waves in critical Abelian gauge theories

Emmanuel Hebey

doi:10.3934/dcds.2012.32.1747

Article Contents

2012, Volume 32, Issue 5: 1747-1761. Doi: 10.3934/dcds.2012.32.1747

This issue Previous Article On a nonlocal parabolic problem arising in electrostatic MEMS control Next Article Schubart-like orbits in the Newtonian collinear four-body problem: A variational proof

Solitary waves in critical Abelian gauge theories

Emmanuel Hebey^1,

1.
Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex

Received: October 31, 2010

Revised: May 31, 2011

Published: April 2012

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Abstract

We prove existence of standing waves solutions for electrostatic Klein-Gordon-Maxwell systems in arbitrary dimensional compact Riemannian manifolds with boundary for zero Dirichlet boundary conditions. We prove that phase compensation holds true when the dimension $n = 3$ or $4$. In these dimensions, existence of a solution is obtained when the mass of the particle field, balanced by the phase, is small in a geometrically quantified sense. In particular, existence holds true for sufficiently large phases. When $n \ge 5$, existence of a solution is obtained when the mass of the particle field is sufficiently small.

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Mathematics Subject Classification: Primary: 35J62, 35J47; Secondary: 35J20.

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