Level Sets of Neumann Eigenfunctions

In this paper we prove that the level sets of the first non–constant eigenfunction of the Neumann Laplacian on a convex planar domain have only finitely many connected components. This problem is motivated, in part, by the "hot spots" conjecture of J. Rauch.

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Veröffentlicht in:	Indiana University mathematics journal 2006-01, Vol.55 (3), p.923-939
Hauptverfasser:	Bañuelos, Rodrigo, Pang, Michael M.H.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analytic functions Boundary conditions College mathematics Continuous functions Eigenfunctions Eigenvalues Exact sciences and technology Laplacians Mathematical analysis Mathematical functions Mathematical theorems Mathematics Partial differential equations Rectangles Sciences and techniques of general use
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Zusammenfassung:	In this paper we prove that the level sets of the first non–constant eigenfunction of the Neumann Laplacian on a convex planar domain have only finitely many connected components. This problem is motivated, in part, by the "hot spots" conjecture of J. Rauch.
ISSN:	0022-2518 1943-5258
DOI:	10.1512/iumj.2006.55.2808