Equidistribution of Neumann data mass on simplices and a simple inverse problem

H Christianson, D Pezzi - Journal of Differential Equations, 2024 - Elsevier

In this paper, we continue the study of eigenfunctions on triangles initiated by the first author
in [2] and [3]. The Neumann data of Dirichlet eigenfunctions on triangles enjoys an …

Asymptotic boundary observability for the wave equation on one side of a planar triangle

H Christianson, E Stafford - Annales Henri Poincaré, 2019 - Springer

We consider the wave equation (∂ _t^ 2-Δ) u= 0 (∂ t 2-Δ) u= 0 on a planar triangular
domain Ω ⊂ R^ 2 Ω⊂ R 2 with Dirichlet boundary conditions. We use a commutator and …

被引用次数：4 相关文章所有 5 个版本

[PDF] arxiv.org

Rellich–Christianson type identities for the Neumann data mass of Dirichlet eigenfunctions on polytopes

A Métras - Annales mathématiques du Québec, 2018 - Springer

We consider the Dirichlet eigenvalue problem on a polytope. We use the Rellich identity to
obtain an explicit formula expressing the Dirichlet eigenvalue in terms of the Neumann data …

被引用次数：4 相关文章所有 3 个版本

[PDF] arxiv.org

Neumann data mass on perturbed triangles

H Christianson, J Xi - arXiv preprint arXiv:1908.02863, 2019 - arxiv.org

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) …

被引用次数：2 相关文章所有 3 个版本

[PDF] arxiv.org

Kuttler-Sigillito's Inequalities and Rellich-Christianson Identity

SM Berge - arXiv preprint arXiv:2110.06801, 2021 - arxiv.org

This article has two main objectives. The first one is to show Kuttler-Sigillito's type
inequalities involving the mixed Neumann-Dirichlet, mixed Steklov-Dirichlet, and mixed …

Quantitative Unique Continuation and Eigenvalue Bounds for the Laplacian

SM Berge - 2021 - ntnuopen.ntnu.no

In this thesis, we are going to study several aspects of the Laplace operator, especially
related to eigenvalues and eigenfunctions. A large part of the thesis is dedicated to …

[PDF] arxiv.org