The size of the first eigenfunction of a convex planar domain
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- by Daniel Grieser and David Jerison PDF
- J. Amer. Math. Soc. 11 (1998), 41-72 Request permission
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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- Daniel Grieser
- Affiliation: Humboldt Universität Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany
- MR Author ID: 308546
- Email: email@example.com
- David Jerison
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Email: firstname.lastname@example.org
- 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 1998 American Mathematical Society
- 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