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• W330399164 abstract "We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field u are prescribed in an open, bounded, Sobolev-class domain $${Omega subseteq mathbb{R}^{rm n}}$$ , and either the normal component $${{bf u} cdot {bf N}}$$ or the tangential components of the vector field $${{bf u} times {bf N}}$$ are prescribed on the boundary $${partial Omega}$$ . For $${{rm k} > {rm n}/2}$$ , we prove that u is in the Sobolev space $${H^{rm k+1}(Omega)}$$ if $${Omega}$$ is an $${H^{rm k+1}}$$ -domain, and the divergence, curl, and either the normal or tangential trace of u has sufficient regularity. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients, and with a rather general set of Dirichlet and Neumann boundary conditions. The resulting regularity theory for the vector u is fundamental in the analysis of free-boundary and moving interface problems in fluid dynamics." @default.
• W330399164 created "2016-06-24" @default.
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• W330399164 date "2016-09-12" @default.
• W330399164 modified "2023-09-26" @default.
• W330399164 title "Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains" @default.
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• W330399164 doi "https://doi.org/10.1007/s00021-016-0289-y" @default.
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