Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/6541
Title: Parabolicity and existence of bounded or dirichlet finite polyharmonic functions
Authors: Wang, Cecilia
Sario, Leo
Mirsky, Norman
Issue Date: 1974
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: Norman Mirsky, Leo Sario, Cecilia Wang, "Cecilia Parabolicity and existence of bounded or dirichlet finite polyharmonic functions", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 6 (1974), pp. 41-50.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
6 (1974)
Abstract: 
Sia $H^{k}$la classe delle funzioni poliarmoniche non degeneri d'ordine
$k$ , cioè delle soluzioni $u$ di $\Delta^{k}u=0,\triangle^{k-1}u\neq0$,
con $k$ un intero $\geq2$ e $\triangle$l'operatore di Laplace-Beltrami
$d\delta+\delta^{d}.$Siano poi $X=B,D,C$ le classi di funzioni che
sono rispettivamente limitate, finite secondo Dirichlet e limitate
e finite secondo Dirichlet; si indichino inoltre con $H^{k}X$ le
corrispondenti sottoclassi di $H^{k}.$Mostreremo che per ogni $H^{k}X-funzioni$
ed anche varietà che non lo sono.

Denote by $H^{k}$the class of nondegenerate polyharmonic functions
of order $k$, that is, solutions $u$ of $\Delta^{k}u=0,\triangle^{k-1}u\neq0$
, $k$ an integer $\geq2$, and $\triangle$the Laplace-Beltrami operator
$d\delta+\delta^{d}$. Let $X=B,D,C$ be the classes of functions
which are bounded, Dirichlet finite, and bounded Dirichlet finite,
respectively, and designate by $H^{k}X$ the corresponding subclasses
of $H^{k}$. We shall show that for every $N\geq2$ and$k\geq2$,
there exist parabolic (and hyperbolic) $N-manifolds$ which carry
$H^{k}X-functions$ , and also such manifolds that do not.
Type: Article
URI: http://hdl.handle.net/10077/6541
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.06 (1974)

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