# On an $H^r(\curl,\O)$ estimate for a Maxwell-type system in convex domains

## TL;DR

This paper establishes regularity estimates for vector fields in convex domains with applications to Maxwell-type systems, enhancing understanding of boundary value problems in electromagnetic theory.

## Contribution

It provides new $H^r( ext{curl})$ estimates for Maxwell systems in convex domains, considering inhomogeneous boundary conditions, extending previous regularity results.

## Key findings

- Regularity estimates for vector fields in convex domains
- $H^r( ext{curl})$ estimates for Maxwell systems
- Application to inhomogeneous boundary conditions

## Abstract

In bounded convex domains, the regularity estimates of a vector field $\u$ with its $\dv\u$, $\curl\u$ in $L^r$ space and the tangential components or the normal component of $\u$ over the boundary in $L^r$ space, are established for $1<r<\infty$. As an application, we derive an $H^r(\curl,\O)$ estimate for solutions to a Maxwell-type system with an inhomogeneous boundary condition in convex domains.