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

• Autorzy: Ikuko Miyamoto , Hidenobu Yoshida
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

cylinder; Neumann problem; harmonic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 74
• Numer: 1
• Strony: 229-235

Daty

wydano

2000

otrzymano

1999-04-25

Twórcy

autor

Ikuko Miyamoto

• Department of Mathematics and Informatics, Chiba University, Chiba 263-8522, Japan

autor

Hidenobu Yoshida

• Department of Mathematics and Informatics, Chiba University, Chiba 263-8522, Japan

Bibliografia

• [1] M. G. Bouligand, Sur les fonctions de Green et de Neumann du cylindre, Bull. Soc. Math. France 42 (1914), 168-242.
• [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.
• [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.
• [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.