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

DOI:
https://doi.org/10.1090/S0002-9947-00-02546-0

Published electronically:
February 16, 2000

MathSciNet review:
1694293

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-00-02546-0

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