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Rough isometry and p-harmonic boundaries of complete Riemannian manifolds

Title
Rough isometry and p-harmonic boundaries of complete Riemannian manifolds
Authors
Lee Y.H.
Ewha Authors
이영하이용하
SCOPUS Author ID
이영하scopus; 이용하scopus
Issue Date
2005
Journal Title
Potential Analysis
ISSN
0926-2601JCR Link
Citation
vol. 23, no. 1, pp. 83 - 97
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In this paper, we describe the behavior of bounded energy finite solutions for certain nonlinear elliptic operators on a complete Riemannian manifold in terms of its p-harmonic boundary. We also prove that if two complete Riemannian manifolds are roughly isometric to each other, then their p-harmonic boundaries are homeomorphic to each other. In the case, there is a one to one correspondence between the sets of bounded energy finite solutions on such manifolds. In particular, in the case of the Laplacian, it becomes a linear isomorphism between the spaces of bounded harmonic functions with finite Dirichlet integral on the manifolds. © Springer 2005.
DOI
10.1007/s11118-004-3261-z
Appears in Collections:
사범대학 > 수학교육과 > Journal papers
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