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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The size of the first eigenfunction
of a convex planar domain


Authors: Daniel Grieser and David Jerison
Journal: J. Amer. Math. Soc. 11 (1998), 41-72
MSC (1991): Primary 35J25, 35B65; Secondary 35J05
MathSciNet review: 1470858
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Abstract: This paper estimates the size of the first Dirichlet eigenfunction of a convex planar domain. The eigenfunction is shown to be well-approximated, uniformly for all convex domains, by the first Dirichlet eigenfunction of a naturally associated ordinary differential (Schrödinger) operator. In particular, the place where the eigenfunction attains its maximum is located to within a distance comparable to the inradius.


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Additional Information

Daniel Grieser
Affiliation: Humboldt Universität Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany
Email: grieser@mathematik.hu-berlin.de

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/S0894-0347-98-00254-9
PII: S 0894-0347(98)00254-9
Keywords: Convex domains, eigenfunctions
Received by editor(s): February 17, 1997
Additional Notes: The first author was a member of the Mathematical Sciences Research Institute, Berkeley. The second author was partially supported by NSF grants DMS-9401355 and DMS-9705825.
Article copyright: © Copyright 1998 American Mathematical Society