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Regularity of the solutions of elliptic systems in polyhedral domains. (English) Zbl 0918.35031

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”.

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
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