Geodesic
On Neumann eigenfunctions in lip domains
Atar, Rami1 ; Burdzy, Krzysztof2
1 Department of Electrical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel
2 Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
Journal of the American Mathematical Society, Tome 17 (2004) no. 2, pp. 243-265

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

A “lip domain” is a planar set lying between graphs of two Lipschitz functions with constant 1. We show that the second Neumann eigenvalue is simple in every lip domain except the square. The corresponding eigenfunction attains its maximum and minimum at the boundary points at the extreme left and right. This settles the “hot spots” conjecture for lip domains as well as two conjectures of Jerison and Nadirashvili. Our techniques are probabilistic in nature and may have independent interest.
DOI : 10.1090/S0894-0347-04-00453-9

Atar, Rami 1 ; Burdzy, Krzysztof 2

1 Department of Electrical Engineering, Technion–Israel Institute of Technology, Haifa 32000, Israel
2 Department of Mathematics, University of Washington, Seattle, Washington 98195-4350 
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Atar, Rami; Burdzy, Krzysztof. On Neumann eigenfunctions in lip domains. Journal of the American Mathematical Society, Tome 17 (2004) no. 2, pp. 243-265. doi: 10.1090/S0894-0347-04-00453-9

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