Neumann Data Mass on Perturbed Triangles

Hans Christianson; Jin Xi

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arXiv · 1908.02863

Neumann Data Mass on Perturbed Triangles

Hans Christianson·Jin Xi

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Abstract

Based on a previous paper [Chr17] on Neumann data for Dirichlet eigenfunctions on triangles, we extend the study in two ways. First, we investigate the (semi-classical) Neumann data mass on perturbed triangles. Specifically, we replace one side of a triangle by adding a smooth perturbation, and assume that the disparity between the perturbation and the original side is bounded by a small value $\epsilon$. Second, we add a small $\epsilon$ sized potential to the (semi-classical) Laplacian and see how the results change on triangles. In both cases, we find that the $L^2$ norm of Neumann data on each side is close to the length of the side divided by the area of the triangle, and the difference is dominated by $\epsilon$.

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Hans Christianson, Jin Xi. 2019-08-07. Neumann Data Mass on Perturbed Triangles. https://arxiv.org/abs/1908.02863

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