An equivalence between the Dirichlet and the Neumann problem for the Laplace operator

DOI10.1007/s11118-015-9524-zzbMath1342.31005OpenAlexW2298012172MaRDI QIDQ283430

Lucian Beznea, Nicolae Radu Pascu, Mihai Nicolae Pascu

Publication date: 13 May 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-015-9524-z

zbMATH Keywords

Dirichlet problemLaplace operatorNeumann problemDirichlet-to-Neumann operatorinfinite-dimensional Laplace operator

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (5)

On non-homogeneous Robin reflection for harmonic functions ⋮ On the relation between weak solutions of elliptic Dirichlet and Neumann boundary-value problems for plane simply connected domains ⋮ On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc ⋮ Brosamler's formula revisited and extensions ⋮ Connections Between the Dirichlet and the Neumann Problem for Continuous and Integrable Boundary Data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Potential theory of infinite dimensional Lévy processes
• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• Partial differential equations. II: Qualitative studies of linear equations
• Classical Dirichlet forms on topological vector spaces - the construction of the associated diffusion process
• Potential theory on Hilbert space
• Harmonic functions on Hilbert space
• A probalistic solution of the Neumann problem.
• Diffusions and Elliptic Operators
• Inverse problems for partial differential equations

This page was built for publication: An equivalence between the Dirichlet and the Neumann problem for the Laplace operator