Some harmonic Robin functions in the complex plane

DOI10.1515/APAM.2010.003zbMath1195.31004MaRDI QIDQ3564951

Tatyana Vaitekhovich, Heinrich Begehr

Publication date: 27 May 2010

Published in: Advances in Pure and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

explicit representationRobin functionRobin boundary value problemcircular ring domain

Mathematics Subject Classification ID

Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items

Representation of the Green's function of the exterior Neumann problem for the Laplace operator ⋮ Integral Representations Related to Complex Partial Differential Operators ⋮ Integral representations in the complex plane and iterated boundary value problems ⋮ Representation of Green’s function of the Neumann problem for a multi-dimensional ball ⋮ Polyharmonic Robin problem for complex linear partial differential equations ⋮ Real variable Hele-Shaw problem with kinetic undercooling ⋮ Fundamental Solutions to the Laplacian in Plane Domains Bounded by Ellipses ⋮ Stability estimates for recovering the potential by the impedance boundary map ⋮ The Robin function and conformal welding -- a new proof of the existence ⋮ Modified harmonic Robin function ⋮ How to find harmonic Green functions in the plane ⋮ Schwarz problem for bi-analytic functions in multiply connected domains ⋮ Dirichlet problem for a generalized inhomogeneous polyharmonic equation in an annular domain ⋮ Iterated Robin problem for the higher-order Poisson equation

Cites Work

• The third boundary condition -- was it Robin's?
• Boundary value problems to first-order complex partial differential equations in a ring domain
• Iterated Neumann problem for the higher order Poisson equation