Asymptotic Dirichlet problem for the $p$-Laplacian on Cartan-Hadamard manifolds
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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 $h.$References
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Additional Information
- Ilkka Holopainen
- Affiliation: Department of Mathematics, P.O. Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland
- MR Author ID: 290418
- Email: ilkka.holopainen@helsinki.fi
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3393-3400
- MSC (2000): Primary 58J60; Secondary 53C20, 31C12
- DOI: https://doi.org/10.1090/S0002-9939-02-06538-3
- MathSciNet review: 1913019