# 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

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topMiyamoto, 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] 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] T. Carleman, Propriétés asymptotiques des fonctions fondamentales des membranes vibrantes, C. R. Skand. Math. Kongress 1934, 34-44.
- [3] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1977. Zbl0361.35003
- [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] 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] D. V. Widder, Functions harmonic in a strip, Proc. Amer. Math. Soc. 12 (1961), 67-72. Zbl0096.07703

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