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We provide a self-contained proof of the solvability and regularity of aHodge-type elliptic system, wherein the divergence and curl of a vector fieldare prescribed in an open, bounded, Sobolev-class domain, and either the normalcomponent or the tangential components of the vector field are prescribed onthe boundary. The proof is based on a regularity theory for vector ellipticequations set on Sobolev-class domains and with Sobolev-class coefficients.

Solvability and regularity for an elliptic system prescribing the curl, divergence, and partial trace of a vector field on Sobolev-class domains