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On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc

On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc

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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 PhysicsSpringer Journals

Published: May 23, 2019

References