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Eigenvalues of weighted $ p$-Laplacian


Author: Lihan Wang
Journal: Proc. Amer. Math. Soc. 141 (2013), 4357-4370
MSC (2010): Primary 53-XX
DOI: https://doi.org/10.1090/S0002-9939-2013-11742-9
Published electronically: August 16, 2013
MathSciNet review: 3105878
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Abstract: In a paper by Z. Lu and J. Rowlett, it is shown that the eigenvalues of the weighted Laplacian can be approximated by eigenvalues of a naturally associated family of narrow graphs. In this paper, we generalize this result to the $ p$-Laplacian. Our approach features overcoming the nonlinearity of the $ p$-Laplacian when $ p\neq 2$, which is different from the Laplacian case.


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Additional Information

Lihan Wang
Affiliation: Department of Mathematics, University of California Irvine, Irvine, California 92697
Email: lihanw@uci.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11742-9
Keywords: $p$-Laplacian, eigenvalue, smooth metric space
Received by editor(s): February 8, 2012
Published electronically: August 16, 2013
Additional Notes: This research was partially supported by NSF grant DMS-0801988
Communicated by: Lei Ni
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.