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The size of the first eigenfunction of a convex planar domain
Author(s):
Daniel
Grieser;
David
Jerison
Journal:
J. Amer. Math. Soc.
11
(1998),
41-72.
MSC (1991):
Primary 35J25, 35B65;
Secondary 35J05
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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:
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.
Copyright of article:
Copyright
1998,
American Mathematical Society
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