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Asymptotic Dirichlet problem for the  -Laplacian on Cartan-Hadamard manifolds
Author(s):
Ilkka
Holopainen
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3393-3400.
MSC (2000):
Primary 58J60;
Secondary 53C20, 31C12
Posted:
March 29, 2002
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Abstract:
We show the existence of nonconstant bounded  -harmonic functions on Cartan-Hadamard manifolds of pinched negative curvature by solving the asymptotic Dirichlet problem at infinity for the  -Laplacian. More precisely, we prove that given a continuous function  on the sphere at infinity there exists a unique  -harmonic function  on  with boundary values 
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Additional Information:
Ilkka
Holopainen
Affiliation:
Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland
Email:
ilkka.holopainen@helsinki.fi
DOI:
10.1090/S0002-9939-02-06538-3
PII:
S 0002-9939(02)06538-3
Keywords:
Cartan-Hadamard manifold,
$p$-harmonic function
Received by editor(s):
June 14, 2001
Posted:
March 29, 2002
Additional Notes:
The author was supported in part by the Academy of Finland, projects 6355 and 44333.
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2002,
American Mathematical Society
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