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On the self-conjugateness of differential forms on bounded domains
Volume 60, no. 1 (2019), pp. 247–256

Abstract

Suppose $\Omega$ is a bounded domain in $\mathbb{R}^n$ with boundary $\Gamma$ and let $\mathcal{W}$ be a non-homogeneous differential form harmonic in $\Omega$ and Hölder-continuous in $\Omega\cup\Gamma$. In this paper we study and obtain some necessary and sufficient conditions for the self-conjugateness of $\mathcal{W}$ in terms of its boundary value $\mathcal{W}|_\Gamma=\omega$.