We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann
boundary conditions by adjusting the shape of the domain on which the eigenvalue problem …

Modification of optical phonon spectra in contacting nonpolar nanoparticles compared to
single particles is studied. Optical phonons in dielectric and semiconducting particles obey …

We prove that among all doubly connected domains of ℝ n of the form, where B 1 and B 2
are open balls of fixed radii such that, the first nonzero Steklov eigenvalue achieves its …

We consider a weighted eigenvalue problem for the Dirichlet laplacian in a smooth bounded
domain Ω⊂ RN, where the bang–bang weight equals a positive constant m¯ on a ball B⊂ Ω …

The composite plate problem is an eigenvalue optimization problem related to the fourth
order operator (− Δ) 2. In this paper we continue the study started in [10], focusing on …

In this paper, we study the first eigenvalue of the Laplacian on doubly connected domains
when Robin and Dirichlet conditions are imposed on the outer and the inner part of the …

In this paper, we study the first eigenvalue of the Laplacian on doubly connected domains
when Robin and Dirichlet conditions are imposed on the outer and the inner part of the …

We formulate a generalization of the Laplace equation under Robin boundary conditions on
a large class of possibly nonsmooth domains by dealing with the trace term appearing in the …

In this paper we address the problem of the minimization of the k-th Robin
eigenvalue\(\lambda _ {k,\beta}\) with parameter\(\beta> 0\) among bounded open Lipschitz …

These lecture notes give an overview of “isoperimetric inequalities”, namely inequalities
involving only geometric features, for the eigenvalues of the Laplace operator, with Dirichlet …