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 …

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 …

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 …

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) …

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 …

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 …

We consider the Schr\"{o} dinger equation $(i\partial_t+\Delta) u= 0$ on an $ n $-
dimensional simplex with Dirichlet boundary conditions. We use a commutator argument …

In this paper, we consider the wave equation on an n-dimensional simplex with Dirichlet
boundary conditions. Our main result is an asymptotic observability identity from any one …

Ce mémoire est composé de trois parties: dans la première, des inégalités spectrales en
lien avec la constante de Cheeger et de Jammes-Cheeger, son équivalent pour le problème …

ASYMPTOTIC BOUNDARY OBSERVABILITY FOR THE WAVE EQUATION ON SIMPLICES By
Ziqing Lu Senior Thesis Department of Mathematics Univer Page 1 ASYMPTOTIC BOUNDARY …