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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Locating the first nodal linein the Neumann problem


Author: David Jerison
Journal: Trans. Amer. Math. Soc. 352 (2000), 2301-2317
MSC (1991): Primary 35J25, 35B65; Secondary 35J05
Published electronically: February 16, 2000
MathSciNet review: 1694293
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Abstract: The location of the nodal line of the first nonconstant Neumann eigenfunction of a convex planar domain is specified to within a distance comparable to the inradius. This is used to prove that the eigenvalue of the partial differential equation is approximated well by the eigenvalue of an ordinary differential equation whose coefficients are expressed solely in terms of the width of the domain. A variant of these estimates is given for domains that are thin strips and satisfy a Lipschitz condition.


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Additional Information

David Jerison
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: jerison@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02546-0
PII: S 0002-9947(00)02546-0
Keywords: Convex domains, eigenfunctions
Received by editor(s): July 7, 1997
Received by editor(s) in revised form: December 15, 1997
Published electronically: February 16, 2000
Additional Notes: The author was partially supported by NSF grants DMS-9401355 and DMS-9705825. The author thanks the referee for many corrections and for suggestions to improve the exposition.
Article copyright: © Copyright 2000 American Mathematical Society