3 papers
math.AP2016
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…
math.AP2016
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…
math.AP2016
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…