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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © 2019 by Springer Nature Switzerland AG
- Subject
- Mathematics; Analysis; Mathematical Methods in Physics
- ISSN
- 1664-2368
- eISSN
- 1664-235X
- DOI
- 10.1007/s13324-019-00314-w
- Publisher site
- See Article on Publisher Site
Abstract
According to the Schwarz symmetry principle, every harmonic function vanishing on a real-analytic curve has an odd continuation, while a harmonic function satisfying homogeneous Neumann condition has an even continuation. Using a technique of Dirichlet to Neumann and Robin to Neumann operators, we derive reflection formulae for non-homogeneous Neumann and Robin conditions from a reflection formula subject to a non-homogeneous Dirichlet condition.
Journal
Analysis and Mathematical Physics – Springer Journals
Published: May 23, 2019