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 …

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

This book serves as an introductory text to optimization theory in normed spaces and covers
all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the …

The global-in-time existence of bounded weak solutions to a large class of physically
relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is …

Shape gradients of PDE constrained shape functionals can be stated in two equivalent
ways. Both rely on the solutions of two boundary value problems (BVPs), but one involves …

We present a method for automatic generation of 3D models based on shape and topology
optimization. The optimization procedure, or model generation process, is initialized by a set …

Mathematical analysis and numerical solutions of problems with unknown shapes or
geometrical domains is a challenging and rich research field in the modern theory of the …

Abstract The classical Faber–Krahn inequality asserts that balls (uniquely) minimize the first
eigenvalue of the Dirichlet Laplacian among sets with given volume. In this article we prove …

In this paper we solve an open problem concerning the characterization of those
measurable sets Ω⊂ R 2 d that, among all sets having a prescribed Lebesgue measure, can …