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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic Dirichlet problem for the $p$-Laplacian on Cartan-Hadamard manifolds


Author: Ilkka Holopainen
Journal: Proc. Amer. Math. Soc. 130 (2002), 3393-3400
MSC (2000): Primary 58J60; Secondary 53C20, 31C12
Published electronically: March 29, 2002
MathSciNet review: 1913019
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Abstract: We show the existence of nonconstant bounded $p$-harmonic functions on Cartan-Hadamard manifolds of pinched negative curvature by solving the asymptotic Dirichlet problem at infinity for the $p$-Laplacian. More precisely, we prove that given a continuous function $h$ on the sphere at infinity there exists a unique $p$-harmonic function $u$ on $M$with boundary values $h.$


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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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2002 American Mathematical Society