Existence and a priori bounds for electrostatic Klein-Gordon-Maxwell systems in fully inhomogeneous spaces

2010/12/16 by Druet, Olivier, Hebey, Emmanuel
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1012.3715

Abstract

We prove existence and uniform bounds for electrostatic Klein-Gordon-Maxwell systems in the inhomogeneous context of a compact Riemannian manifold when the mass potential, balanced by the phase, is small in a quantified sense.

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• Klein-Gordon-Maxwell equations in high dimensions
• Dirichlet and Neumann problems for Klein-Gordon-Maxwell systems
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• Improved estimates and a limit case for the electrostatic Klein-Gordon-Maxwell system
• Geometric inequalities for electrostatic systems with boundary