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

Since the early part of the twentieth century, the use of integral equations has developed into
a range of tools for the study of partial differential equations. This includes the use of single …

The fields of photonics and phononics encompass the fundamental science of light and
sound propagation and interactions in complex structures, as well as its technological …

Meta-materials are assemblies of small components. Even though the single component
consists of ordinary materials, the meta-material may behave effectively in a way that is not …

Abstract Contents Introduction Chapter I. Surface potentials in the Helmholtz resonator
problem § 1.1. Preliminary results for limiting problems § 1.2. Existence of poles with small …

In this paper we obtain the continuity of attractors for semilinear parabolic problems with
Neumann boundary conditions relatively to perturbations of the domain. We show that, if the …

This text is the written version of lectures on resonances given at the Mathematics
department of the Gothenburg University and Chalmers in the Spring semesters of 2000 to …

We obtain the first term in the asymptotic expansion of the eigenvalues of the Laplace
operator in a typical dumbbell domain in ${\mathbb {R}^ 2} $. This domain consists of two …

We consider the Neumann boundary-value problem of finding the small-parameter
asymptotics of the eigenvalues and eigenfunctions for the Laplace operator in a singularly …

We analyse the spectrum of the Laplace operator in a complex geometry, representing a
small Helmholtz resonator. The domain is obtained from a bounded set Ω⊂ R n by removing …