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

@article{AIF_1971__21_3_217_0,
     author = {Kwon, Y. K. and Sario, Leo and Walsh, Bertram},
     title = {Behavior of biharmonic functions on Wiener's and Royden's compactifications},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {21},
     number = {3},
     year = {1971},
     pages = {217-226},
     doi = {10.5802/aif.387},
     zbl = {0208.13703},
     mrnumber = {49 \#5385},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1971__21_3_217_0}
}
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/item/AIF_1971__21_3_217_0/

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