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Lord Rayleigh’s Conjecture for Vibrating Clamped Plates in Positively Curved Spaces
We affirmatively solve the analogue of Lord Rayleigh’s conjecture on Riemannian manifolds with positive Ricci curvature for any clamped plates in 2...
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On a Nonlinear Dirichlet Eigenvalue Problem
In this work, considering a mixed operator composed of the p-Laplacian and the Laplacian, we study a generalized spectral problem with Dirichlet...
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A Faber-Krahn inequality for mixed local and nonlocal operators
We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn...
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The Negative Spectrum of the Robin Laplacian
In this article we review various results about the negative spectrum of the Laplacian with a mixed attractive Robin boundary condition.
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Quantum mechanics, radiation, and the equivalence proof
This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence...
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The Laplacian with Boundary Conditions
The abstract theory developed in previous chapters is applied to the spectral theory of the Laplacian on a bounded open set in Euclidean space. We...
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Studies on the Zeroes of Bessel Functions and Methods for Their Computation: IV. Inequalities, Estimates, Expansions, etc., for Zeros of Bessel Functions
This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities,...
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The clamped plate in Gauss space
In this paper, we study the analogue in Gauss space of Lord Rayleigh’s conjecture for the clamped plate. We show that the first eigenvalue of the...
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Fluid Dynamics
One important source of dynamic transitions and pattern formation is transition and stability problems in fluid dynamics, including in particular...
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Global bifurcation of steady gravity water waves with critical layers
We construct families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a...
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Tosio Kato’s work on non-relativistic quantum mechanics: part 1
We review the work of Tosio Kato on the mathematics of non-relativistic quantum mechanics and some of the research that was motivated by this. Topics...
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Optimal shape of a domain which minimizes the first buckling eigenvalue
In this paper we prove the existence of an optimal domain which minimizes the buckling load of a clamped plate among all bounded domains with given...
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From Johannes D. van der Waals, 8 March 1878
’T is met de levendigste belangstelling en groote erkentelijkheid, dat ik gelezen heb de redevoering, die u de goedheid gehad hebt mij toe te zenden.
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The eigenvalues of the Laplacian with Dirichlet boundary condition in \(\mathbb {R}^2\) are almost never minimized by disks
Minimization of the Dirichlet eigenvalues of the Laplacian among sets of prescribed measure is a standard problem in shape optimization. The main...
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Fluid Dynamics
One important source of dynamic transitions and pattern formation is transition and stability problems in fluid dynamics, including in particular...
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Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator
The purpose of this manuscript is to present a series of lecture notes on isoperimetric inequalities for the Laplacian, for the Schrödinger operator,...
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Krahn’s proof of the Rayleigh conjecture revisited
The paper is a discussion of Krahn’s proof of the Rayleigh conjecture that amongst all membranes of the same area and the same physical properties,...
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Models of Higher Order
The goal of this chapter is to explain in some detail which models and equations are considered in this book and to provide some background...
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Eigenvalue Problems
For quite general second order elliptic operators onemay use themaximumprinciple and the Kreĭn-Rutman theorem to show that the...