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Solutions of a certain nonlinear elliptic equation on Riemannian manifolds

Title
Solutions of a certain nonlinear elliptic equation on Riemannian manifolds
Authors
Lee Y.H.
Ewha Authors
이용하
SCOPUS Author ID
이용하scopus
Issue Date
2001
Journal Title
Nagoya Mathematical Journal
ISSN
0027-7630JCR Link
Citation
vol. 162, pp. 149 - 167
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In this paper, we prove that if a complete Riemannian manifold M has finitely many ends, each of which is a Harnack end, then the set of all energy finite bounded A-harmonic functions on M is one to one corresponding to Rl, where A is a nonlinear elliptic operator of type p on M and l is the number of p-nonparabolic ends of M. We also prove that if a complete Riemannian manifold M is roughly isometric to a complete Riemannian manifold with finitely many ends, each of which satisfies the volume doubling condition, the Poincaré inequality and the finite covering condition near infinity, then the set of all energy finite bounded A-harmonic functions on M is finite dimensional. This result generalizes those of Yau, of Donnelly, of Grigor'yan, of Li and Tam, of Holopainen, and of Kim and the present author, but with a barrier argument at infinity that the peculiarity of nonlinearity demands.
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사범대학 > 수학교육과 > Journal papers
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