ArticleOriginal scientific text

Title

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

Authors 1, 1

Affiliations

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

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.

Keywords

cylinder, Neumann problem, harmonic functions

Bibliography

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  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.
Pages:
229-235
Main language of publication
English
Received
1999-04-25
Published
2000
Exact and natural sciences