The size of the first eigenfunction of a convex planar domain

Grieser, Daniel; Jerison, David

doi:10.1090/S0894-0347-98-00254-9

The size of the first eigenfunction of a convex planar domain
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by Daniel Grieser and David Jerison

J. Amer. Math. Soc. 11 (1998), 41-72

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

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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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