Lower bounds for interior nodal sets of Steklov eigenfunctions
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- by Christopher D. Sogge, Xing Wang and Jiuyi Zhu PDF
- Proc. Amer. Math. Soc. 144 (2016), 4715-4722 Request permission
Abstract:
We study the interior nodal sets, $Z_\lambda$ of Steklov eigenfunctions in an $n$-dimensional relatively compact manifold $M$ with boundary and show that one has the lower bounds $|Z_\lambda |\ge c\lambda ^{\frac {2-n}2}$ for the size of its $(n-1)$-dimensional Hausdorff measure. The proof is based on a Dong-type identity and estimates for the gradient of Steklov eigenfunctions, similar to those in previous works of the first author and Zelditch.References
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Additional Information
- Christopher D. Sogge
- Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
- MR Author ID: 164510
- Email: sogge@jhu.edu
- Xing Wang
- Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
- Address at time of publication: Department of Mathematics, Wayne State University, Detroit, MI 48202
- MR Author ID: 1123185
- Email: fz1316@wayne.edu
- Jiuyi Zhu
- Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
- Address at time of publication: Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803
- Email: zhu@math.isu.edu
- Received by editor(s): March 16, 2015
- Published electronically: July 22, 2016
- Additional Notes: The first two authors were supported in part by the NSF grant DMS-1361476
The third author was supported in part by the NSF grant DMS-1500468 - Communicated by: Alexander Iosevich
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4715-4722
- MSC (2010): Primary 35-xx
- DOI: https://doi.org/10.1090/proc/13067
- MathSciNet review: 3544523