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Locating the first nodal linein the Neumann problem
Author(s):
David
Jerison
Journal:
Trans. Amer. Math. Soc.
352
(2000),
2301-2317.
MSC (1991):
Primary 35J25, 35B65;
Secondary 35J05
Posted:
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.
References:
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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:
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
Posted:
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.
Copyright of article:
Copyright
2000,
American Mathematical Society
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