Moscow Mathematical Journal

Volume 15, Issue 1, January–March 2015 pp. 101–106.

Eigenfunctions for 2-Dimensional Tori and for Rectangles with Neumann Boundary Conditions

Authors: Thomas Hoffmann-Ostenhof
Author institution:Department of Theoretical Chemistry, A 1090 Wien, Wӓhringerstraße 17, Austria

Summary:

Consider the eigenfunctions u for a 2D-torus, respectively, the free rectangular membrane, so that −∆u = λu on ℛ(c, d) = (0, c) × (0, d) with periodic, respectively, Neumann boundary conditions. In this note we show that if u > 0 on ∂ℛ(c, d) then u ≡ C > 0 in ℛ(c, d).

2010 Math. Subj. Class. 35B05, 35J05.

Keywords: Eigenfunctions, 2D torus, free rectangular membrane.

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