Nicaise, Serge Regularity of the solutions of elliptic systems in polyhedral domains. (English) Zbl 0918.35031 Bull. Belg. Math. Soc. - Simon Stevin 4, No. 3, 411-429 (1997). From author’s abstract: “The solution of the Dirichlet problem relative to an elliptic system in a polyhedron has a complex singular behaviour near edges and vertices. Here, we show that this solution has a global regularity in appropriate weighted Sobolev spaces. Some useful embeddings of these spaces into classical Sobolev spaces are also established. As applications, we consider the LamĂ©, Stokes and Navier-Stokes systems. The present results will be applied in a forthcoming work to the constructive treatment of these problems by optimal convergent finite element method”. Reviewer: G.Di Fazio (Catania) Cited in 18 Documents MSC: 35B65 Smoothness and regularity of solutions to PDEs 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35J67 Boundary values of solutions to elliptic equations and elliptic systems 35B40 Asymptotic behavior of solutions to PDEs Keywords:vertex-edge singularities; global regularity; weighted Sobolev spaces PDFBibTeX XMLCite \textit{S. Nicaise}, Bull. Belg. Math. Soc. - Simon Stevin 4, No. 3, 411--429 (1997; Zbl 0918.35031) Full Text: EuDML