We consider minimizers of where F is a function nondecreasing in each parameter, and λk
(Ω) is the kth Dirichlet eigenvalue of ω. This includes, in particular, functions F that depend …

We develop a computational method for extremal Steklov eigenvalue problems and apply it
to study the problem of maximizing the p th Steklov eigenvalue as a function of the domain …

Recently Fraser and Schoen showed that the solution of a certain extremal Steklov
eigenvalue problem on a compact surface with boundary can be used to generate a free …

We develop methods based on fundamental solutions to compute the Steklov, Wentzell and
Laplace–Beltrami eigenvalues in the context of shape optimization. In the class of smooth …

We consider to solve numerically the shape optimization models with Dirichlet Laplace
eigenvalues. Both volume-constrained and volume unconstrained formulations of the model …

Let (M, g) be a connected, closed, orientable Riemannian surface and denote by λk (M, g)
the kth eigenvalue of the Laplace− Beltrami operator on (M, g). In this paper, we consider the …

In an extremal eigenvalue problem, one considers a family of eigenvalue problems, each
with discrete spectra, and extremizes a chosen eigenvalue over the family. In this chapter …

Let $\Omega\subset\mathbb {R}^ n $ be an open set with same volume as the unit ball $ B $
and let $\lambda_k (\Omega) $ be the $ k $-th eigenvalue of the Laplace operator of …

We perform a numerical optimisation of the low frequencies of the Dirichlet Laplacian with
perimeter and surface area restrictions, in two and 3-dimensions, respectively. In the former …

We consider Steklov eigenvalues of reflection-symmetric, nearly circular, planar domains.
Treating such domains as perturbations of the disc, we obtain a second-order formal …