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On the Self-conjugateness of differential forms on bounded domains. (English) Zbl 1418.30044

Summary: 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 \(\mathcal{W}|_{\Gamma} = \omega\).

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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