Behavior of biharmonic functions on Wiener's and Royden's compactifications
Annales de l'Institut Fourier, Volume 21 (1971) no. 3, pp. 217-226.

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 ΔΔu=0) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.

Soit R une variété riemannienne de volume fini, Δ l’opérateur laplacien sur R. Pour certains sous-espaces des algèbres de Wiener et Royden sur R, on construit une décomposition canonique liée à l’opérateur itéré ΔΔ. Si u est une solution de l’équation biharmonique ΔΔu=0, les valeurs de u et Δu à la frontière idéale déterminent les composantes de u suivant la décomposition.

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     title = {Behavior of biharmonic functions on {Wiener's} and {Royden's} compactifications},
     journal = {Annales de l'Institut Fourier},
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Kwon, Y. K.; Sario, Leo; Walsh, Bertram. Behavior of biharmonic functions on Wiener's and Royden's compactifications. Annales de l'Institut Fourier, Volume 21 (1971) no. 3, pp. 217-226. doi : 10.5802/aif.387. http://www.numdam.org/articles/10.5802/aif.387/

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