Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains

C. H.Arthur Cheng, Steve Shkoller

研究成果: 雜誌貢獻期刊論文同行評審

15 引文 斯高帕斯(Scopus)

摘要

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 Ω ⊆ Rn, and either the normal component u· N or the tangential components of the vector field u× N are prescribed on the boundary ∂Ω. For k > n / 2 , we prove that u is in the Sobolev space Hk + 1(Ω) if Ω is an Hk + 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.

原文???core.languages.en_GB???
頁(從 - 到)375-422
頁數48
期刊Journal of Mathematical Fluid Mechanics
19
發行號3
DOIs
出版狀態已出版 - 1 9月 2017

指紋

深入研究「Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains」主題。共同形成了獨特的指紋。

引用此