Soit une variété riemannienne de volume fini, l’opérateur laplacien sur . Pour certains sous-espaces des algèbres de Wiener et Royden sur , on construit une décomposition canonique liée à l’opérateur itéré . Si est une solution de l’équation biharmonique , les valeurs de et à la frontière idéale déterminent les composantes de suivant la décomposition.
Let be a smooth Riemannian manifold of finite volume, its Laplace (-Beltrami) operator. Canonical direct-sum decompositions of certain subspaces of the Wiener and Royden algebras of are found, and for biharmonic functions (those for which ) the decompositions are related to the values of the functions and their Laplacians on appropriate ideal boundaries.
@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}, volume = {21}, year = {1971}, pages = {217-226}, doi = {10.5802/aif.387}, mrnumber = {49 \#5385}, zbl = {0208.13703}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 21 (1971) pp. 217-226. doi : 10.5802/aif.387. http://gdmltest.u-ga.fr/item/AIF_1971__21_3_217_0/
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