The Schwarz reflection principle for harmonic functions in \(\mathbb R^2\) subject to the Robin condition

DOI10.1016/j.jmaa.2008.08.010zbMath1155.31001OpenAlexW2060167561MaRDI QIDQ950463

Boris P. Belinskiy, Tatiana V. Savina

Publication date: 22 October 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.08.010

zbMATH Keywords

harmonic functionsRobin conditionreflection principle

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Hölder stability estimate of Robin coefficient in corrosion detection with a single boundary measurement ⋮ On non-homogeneous Robin reflection for harmonic functions ⋮ On -reflection of harmonic functions and -approximation by harmonic polynomials ⋮ On non-local reflection for elliptic equations of the second order in $\mathbb{R}^{2}$ (the Dirichlet condition) ⋮ On the Neumann problem for harmonic functions in the upper half plane ⋮ On the dependence of the reflection operator on boundary conditions for biharmonic functions ⋮ Uniqueness to inverse acoustic scattering from coated polygonal obstacles with a single incoming wave

Cites Work

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• Exact and asymptotic solutions of the cauchy problem
• A reflection formula for the Helmholtz equation with the Neumann condition

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