On the existence of solutions for the Maxwell equations

TL;DR

This paper provides mathematical proofs confirming the existence of solutions to Maxwell's equations with appropriate boundary conditions, emphasizing the validity of delayed potentials as effective solutions under certain source conditions.

Contribution

It offers rigorous proofs of solution existence for Maxwell's equations, validating the use of delayed potentials in electromagnetic theory.

Findings

Existence of solutions under suitable boundary conditions

Delayed potentials are effective solutions

Conditions on sources ensure solution validity

Abstract

Mathematical proofs are presented concerning the existence of solutions of the Maxwell equations with suitable boundary conditions. In particular it is stated that the well known "delayed potentials" provide effective solutions of the equations, under reasonable conditions on the sources of the fields.