It is of great importance for the development of new products to find the best possible
topology or layout for given design objectives and constraints at a very early stage of the …

In topology optimization of structures, materials and mechanisms, parametrization of
geometry is often performed by a grey-scale density-like interpolation function. In this paper …

This second edition takes advantage of several comments received by colleagues and
students. With respect to the first edition (published by SIAM in 2006) several new sections …

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 …

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 …

The fascinating? eld 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 …

We consider two-dimensional Schrödinger operators in bounded domains. We analyze
relations between the nodal domains of eigenfunctions, spectral minimal partitions and …

In this Note we give a short review on recent developements in shape optimization. We
explain how the generic non-existence of solutions can be circumvent. Either one can …

For every k ∈ N, we prove the existence of a quasi-open set minimizing the k-th eigenvalue
of the Dirichlet Laplacian among all sets of prescribed Lebesgue measure. Moreover, we …

Here we study the asymptotic limits of solutions of some singularly perturbed elliptic
systems. The limiting problems involve multiple valued harmonic functions or, in general …