# Existence and regularity for eddy currents system with non-smooth conductivity

## TL;DR

This paper establishes the existence, uniqueness, and regularity of solutions for the eddy currents system with non-smooth conductivity, advancing understanding of magneto-quasistatic approximations in electromagnetism.

## Contribution

It proves well-posedness and regularity results for the eddy currents system with bounded measurable conductivity, a case previously not well-understood.

## Key findings

- Existence and uniqueness of weak solutions are established.
- Global Hölder estimates for the magnetic field are provided.
- The results apply to systems with non-smooth, measurable conductivity.

## Abstract

We discuss the well-posedness of the 'transient eddy current' magneto-quasistatic approximation of Maxwell's initial value problem with bounded and measurable conductivity, with sources, on a domain. We prove existence and uniqueness of weak solutions, and we provide global Hoelder estimates for the magnetic part.