Problems linking the shape of a domain or the coefficients of an elliptic operator to the
sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this …

Optimizing the shape of an object to make it the most efficient or the most resistant or the
most streamlined or the lightest or the most noiseless or the most stealthy or the cheapest is …

This paper reviews many of the known inequalities for the eigenvalues of the Laplacian and
bi-Laplacian on bounded domains in Euclidean space. In particular, we focus on …

We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

The fascinating field of shape optimization problems has received a lot of attention in recent
years, particularly in relation to a number of applications in physics and engineering that …

This is a comprehensive review of the nodal domains and lines of quantum billiards,
emphasizing a quantitative comparison of theoretical findings to experiments. The nodal …

Convexity is important in theoretical aspects of mathematics and also for economists and
physicists. In this monograph the author provides a comprehensive insight into convex sets …

Optimization problems involving eigenvalues arise in many different mathematical
disciplines. This article is divided into two parts. Part I gives a historical account of the …

Ce livre est une initiation aux approches modernes de l'optimisation mathématique de
formes. Il s' appuie sur les seules connaissances de première année de Master de …

A bstract We study the perturbative unitarity of scattering amplitudes in general dimensional
reductions of Yang-Mills theories and general relativity on closed internal manifolds. For the …