Static Klein-Gordon-Maxwell-Proca systems in 4-dimensional closed manifolds

TL;DR

This paper proves existence and uniform bounds for static Klein-Gordon-Maxwell-Proca systems in four-dimensional closed manifolds, extending previous work to the double critical case with a massive vector field.

Contribution

It introduces new existence results and bounds for the double critical Klein-Gordon-Maxwell-Proca systems in 4D manifolds, generalizing prior Maxwell-based models.

Findings

Existence of solutions in the double critical case

Uniform bounds for solutions in 4D manifolds

Extension of previous Maxwell-based results to Proca systems

Abstract

Static Klein-Gordon-Maxwell-Proca systems are massive versions of the electrostatic Klein-Gordon-Maxwell Systems. The vector field in these systems inherits a mass and is governed by the Proca action which generalizes that of Maxwell. Following previous work by Druet & al. we prove existence and uniform bounds for such systems in the double critical case of dimension 4.