On quantitative Runge approximation for the time harmonic Maxwell equations

TL;DR

This paper develops quantitative Runge approximation results for the time-harmonic Maxwell equations, providing explicit estimates and analyzing the conditional stability of the associated Cauchy problem.

Contribution

It introduces explicit quantitative Runge approximation results and stability estimates for the time-harmonic Maxwell equations, advancing theoretical understanding.

Findings

Explicit quantitative Runge approximation results derived.

Conditional stability results for the Maxwell Cauchy problem established.

Enhanced understanding of approximation and stability in electromagnetic modeling.

Abstract

Here we derive some results on so called quantitative Runge approximation in the case of the time-harmonic Maxwell equations. This provides a Runge approximation having more explicit quantitative information. We additionally derive some results on the conditional stability of the Cauchy problem for the time-harmonic Maxwell equations.