Harmonic functions in a cylinder with normal derivatives vanishing on the boundary

Ikuko Miyamoto; Hidenobu Yoshida

Annales Polonici Mathematici (2000)

  • Volume: 74, Issue: 1, page 229-235
  • ISSN: 0066-2216

Abstract

top
A harmonic function in a cylinder with the normal derivative vanishing on the boundary is expanded into an infinite sum of certain fundamental harmonic functions. The growth condition under which it is reduced to a finite sum of them is given.

How to cite

top

Miyamoto, Ikuko, and Yoshida, Hidenobu. "Harmonic functions in a cylinder with normal derivatives vanishing on the boundary." Annales Polonici Mathematici 74.1 (2000): 229-235. <http://eudml.org/doc/208368>.

@article{Miyamoto2000,
abstract = {A harmonic function in a cylinder with the normal derivative vanishing on the boundary is expanded into an infinite sum of certain fundamental harmonic functions. The growth condition under which it is reduced to a finite sum of them is given.},
author = {Miyamoto, Ikuko, Yoshida, Hidenobu},
journal = {Annales Polonici Mathematici},
keywords = {cylinder; Neumann problem; harmonic functions; growth condition; series expansion},
language = {eng},
number = {1},
pages = {229-235},
title = {Harmonic functions in a cylinder with normal derivatives vanishing on the boundary},
url = {http://eudml.org/doc/208368},
volume = {74},
year = {2000},
}

TY - JOUR
AU - Miyamoto, Ikuko
AU - Yoshida, Hidenobu
TI - Harmonic functions in a cylinder with normal derivatives vanishing on the boundary
JO - Annales Polonici Mathematici
PY - 2000
VL - 74
IS - 1
SP - 229
EP - 235
AB - A harmonic function in a cylinder with the normal derivative vanishing on the boundary is expanded into an infinite sum of certain fundamental harmonic functions. The growth condition under which it is reduced to a finite sum of them is given.
LA - eng
KW - cylinder; Neumann problem; harmonic functions; growth condition; series expansion
UR - http://eudml.org/doc/208368
ER -

References

top
  1. [1] M. G. Bouligand, Sur les fonctions de Green et de Neumann du cylindre, Bull. Soc. Math. France 42 (1914), 168-242. Zbl45.0592.01
  2. [2] T. Carleman, Propriétés asymptotiques des fonctions fondamentales des membranes vibrantes, C. R. Skand. Math. Kongress 1934, 34-44. 
  3. [3] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1977. Zbl0361.35003
  4. [4] S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242-256. Zbl0041.42701
  5. [5] H. Weyl, Das asymptotische Verteilungsgestez der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung), Math. Ann. 71 (1912), 441-479. 
  6. [6] D. V. Widder, Functions harmonic in a strip, Proc. Amer. Math. Soc. 12 (1961), 67-72. Zbl0096.07703

NotesEmbed ?

top

You must be logged in to post comments.