Behavior of biharmonic functions on Wiener's and Royden's compactifications

Y. K. Kwon; Leo Sario; Bertram Walsh

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 3, page 217-226
  • ISSN: 0373-0956

Abstract

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Let R be a smooth Riemannian manifold of finite volume, Δ its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of R are found, and for biharmonic functions (those for which Δ Δ u = 0 ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.

How to cite

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Kwon, Y. K., Sario, Leo, and Walsh, Bertram. "Behavior of biharmonic functions on Wiener's and Royden's compactifications." Annales de l'institut Fourier 21.3 (1971): 217-226. <http://eudml.org/doc/74049>.

@article{Kwon1971,
abstract = {Let $R$ be a smooth Riemannian manifold of finite volume, $\Delta $ its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of $R$ are found, and for biharmonic functions (those for which $\Delta \Delta u = 0$) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.},
author = {Kwon, Y. K., Sario, Leo, Walsh, Bertram},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {217-226},
publisher = {Association des Annales de l'Institut Fourier},
title = {Behavior of biharmonic functions on Wiener's and Royden's compactifications},
url = {http://eudml.org/doc/74049},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Kwon, Y. K.
AU - Sario, Leo
AU - Walsh, Bertram
TI - Behavior of biharmonic functions on Wiener's and Royden's compactifications
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 3
SP - 217
EP - 226
AB - Let $R$ be a smooth Riemannian manifold of finite volume, $\Delta $ its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of $R$ are found, and for biharmonic functions (those for which $\Delta \Delta u = 0$) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.
LA - eng
UR - http://eudml.org/doc/74049
ER -

References

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  1. [1] S. BERGMAN and M. SCHIFFER, Kernel functions and elliptic differential equations in mathematical physics, Academic Press, New York, (1953), 432 p. Zbl0053.39003MR14,876d
  2. [2] C. CONSTANINESCU and A. CORNEA, Ideale Ränder Riemannscher Flächen, Springer, (1963), 244 p. Zbl0112.30801
  3. [3] P.R. GARABEDIAN, Partial differential equations, Wiley, New York, (1964), 672 p. Zbl0124.30501MR28 #5247
  4. [4] M. NAKAI and L. SARIO, Biharmonic classification of Riemannian manifolds, (to appear). Zbl0253.31011
  5. [5] M. NAKAI and L. SARIO, Quasiharmonic classification of Riemannian manifolds, (to appear). Zbl0229.31006
  6. [6] G. DE RHAM, Variétés différentiables, Hermann, Paris, (1960), 196 p. Zbl0089.08105
  7. [7] L. SARIO — M. NAKAI, Classification theory of Riemann surfaces, Springer, (1970), 446 p. Zbl0199.40603MR41 #8660
  8. [8] L. SARIO — M. SCHIFFER — M. GLASNER, The span and principal functions in Riemannian spaces, J. Analyse Math. 15 (1965), 115-134. Zbl0136.09603MR32 #1655
  9. [9] I.N. VEKUA, New methods for solving elliptic equations, North-Holland, Amsterdam, (1967), 358 p. Zbl0146.34301MR35 #3243

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