Reproducing Kernels for Hilbert Spaces of Real Harmonic Functions

DOI10.1137/080739628zbMath1202.46030OpenAlexW2050094051MaRDI QIDQ4931695

J. F. G. Auchmuty

Publication date: 30 September 2010

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/1dfc79b47bd0bc98b5466f5e15d458f8ce576cd9

zbMATH Keywords

reproducing kernelharmonic functionskernel functionstrace spacesSteklov eigenfunctions

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Other functions defined by series and integrals (33E20) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)

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A novel efficient numerical solution of Laplace equation with mixed boundary conditions ⋮ The S.V.D. of the Poisson kernel ⋮ Steklov representations of Green's functions for Laplacian boundary value problems ⋮ Bounds and representations of solutions of planar div-curl problems ⋮ Highly accurate and efficient numerical methods for a problem of heat conduction ⋮ Robin Approximation of Dirichlet Boundary Value Problems ⋮ Positive solutions of elliptic problems involving both critical Sobolev nonlinearities on exterior regions ⋮ A boundary formula for reproducing kernel Hilbert spaces of real harmonic functions in Lipschitz domains ⋮ Well‐posedness and approximation of solutions of linear divergence‐form elliptic problems on exterior regions ⋮ Boundary Integrals and Approximations of Harmonic Functions ⋮ Steklov approximations of harmonic boundary value problems on planar regions

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