On non-homogeneous Robin reflection for harmonic functions

DOI10.1080/00036811.2021.1994958zbMath1490.31001OpenAlexW3214396944MaRDI QIDQ5072139

Murdhy Aldawsari, Tatiana V. Savina

Publication date: 25 April 2022

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

Full work available at URL: https://doi.org/10.1080/00036811.2021.1994958

zbMATH Keywords

harmonic functionsSchwarz symmetry principleDirichlet-to-Neumann mapRobin-to-Neumann map

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Cites Work

• An equivalence between the Dirichlet and the Neumann problem for the Laplace operator
• Dirichlet-to-Neumann maps on bounded Lipschitz domains
• Reflection principles for linear elliptic second order partial differential equations with constant coefficients
• Qualitative methods in inverse scattering theory. An introduction
• Generalized \(Q\)-functions and Dirichlet-to-Neumann maps for elliptic differential operators
• The Schwarz reflection principle for harmonic functions in \(\mathbb R^2\) subject to the Robin condition
• From reflections to a uniform elliptic growth
• On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc
• An analytical solution of the Laplace equation with Robin conditions by applying Legendre transform
• Linear Holomorphic Partial Differential Equations and Classical Potential Theory
• On non-local reflection for elliptic equations of the second order in $\mathbb{R}^{2}$ (the Dirichlet condition)
• A reflection formula for the Helmholtz equation with the Neumann condition

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