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Properties of some weighted Sobolev spaces and application to spectral approximations. (English) Zbl 0675.65114

The authors discuss the introduction of weighted Sobolev spaces on a square associated with the Jacobi weighted measure. A weighted regularity result for the Dirichlet problem associated with the Laplace operator is also discussed. Several projection operators with polynomial values are considered for which approximation results in weighted norms are stated. Finally, a collocation spectral method for the Dirichlet problem of the Laplace operator with inhomogeneous boundary condition is analyzed. It is also indicated that the authors present new results on Chebyshev approximation.
Reviewer: P.K.Mahanti

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
46M35 Abstract interpolation of topological vector spaces
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