Geodesic
The size of the first eigenfunction of a convex planar domain
Grieser, Daniel1 ; Jerison, David2
1 Humboldt Universität Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Journal of the American Mathematical Society, Tome 11 (1998) no. 1, pp. 41-72

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-98-00254-9

Grieser, Daniel 1 ; Jerison, David 2

1 Humboldt Universität Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 
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Grieser, Daniel; Jerison, David. The size of the first eigenfunction of a convex planar domain. Journal of the American Mathematical Society, Tome 11 (1998) no. 1, pp. 41-72. doi: 10.1090/S0894-0347-98-00254-9

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