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

DOI:
https://doi.org/10.1090/S0894-0347-98-00254-9

MathSciNet review:
1470858

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0894-0347-98-00254-9

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