TY - JOUR
T1 - On Dirichlet to Neumann and Robin to Neumann operators suitable for reflecting harmonic functions subject to a non-homogeneous condition on an arc
AU - Aldawsari, Murdhy
AU - Savina, Tatiana
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
KW - Analytic continuation
KW - Dirichlet to Neumann operator
KW - Robin to Neumann operator
KW - Schwarz symmetry principle
UR - http://www.scopus.com/inward/record.url?scp=85067655856&partnerID=8YFLogxK
U2 - 10.1007/s13324-019-00314-w
DO - 10.1007/s13324-019-00314-w
M3 - Article
AN - SCOPUS:85067655856
SN - 1664-2368
VL - 9
SP - 729
EP - 745
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 2
ER -