Boundary Regularity for an Even Order Elliptic System in the Critical Dimension

TL;DR

This paper proves that weak solutions to a boundary value problem for an even order elliptic system with antisymmetric potential are continuous up to the boundary, under continuous boundary conditions.

Contribution

It establishes boundary regularity for solutions of a specific class of higher-order elliptic systems with antisymmetric potentials.

Findings

Weak solutions are continuous up to the boundary.

Boundary data continuity implies solution continuity at the boundary.

Results apply to systems with antisymmetric first order potentials.

Abstract

In this short note, we consider the Dirichlet problem associated to an even order elliptic system with antisymmetric first order potential. Given any continuous boundary data, we show that weak solutions are continuous up to boundary.