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The S.V.D. of the Poisson Kernel
Giles Auchmuty
This paper describes the singular value decomposition (SVD) of the Poisson kernel for the Dirichlet problem for the Laplacian on bounded regions in R^N, N >=2. This operator is a c…
Bounds and regularity of Solutions of Planar Div-curl Problems
Giles Auchmuty
New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary ar…
Steklov Approximations of Harmonic Boundary Value Problems on Planar Regions
Giles Auchmuty, Manki Cho
Error estimates for approximations of harmonic functions on planar regions by subspaces spanned by the first harmonic Steklov eigenfunctions are found. They are based on the explic…
Laplacian Eigenproblems on Product Regions and Tensor Products of Sobolev Spaces
Giles Auchmuty, M. A. Rivas
Characterizations of eigenvalues and eigenfunctions of the Laplacian on a product domain are obtained. When zero Dirichlet, Robin or Neumann boundary conditions are specified on ea…
Boundary Integrals and Approximations of Harmonic Functions
Giles Auchmuty, Manki Cho
Formulae for the value of a harmonic function at the center of a rectangle are found that involve boundary integrals. The central value of a harmonic function is shown to be well a…