Equidistribution of Neumann data mass on triangles

2017/01/10 by Christianson, Hans
#35P20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1701.02793

Abstract

In this paper we study the behaviour of the Neumann data of Dirichlet eigenfunctions on triangles. We prove that the L² norm of the (semi-classical) Neumann data on each side is equal to the length of the side divided by the area of the triangle. The novel feature of this result is that it is \it not an asymptotic, but an exact formula. The proof is by simple integrations by parts.

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