We study the effect of regular and singular domain perturbations on layer potential operators
for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic …

We consider the Dirichlet problem for the Laplace equation in a planar domain with a small
hole. The diameter of the hole is proportional to a real parameter ε and we denote by u ε the …

Taking advantage from the so-called Lemma on small eigenvalues by Colin de Verdière, we
study ramification for multiple eigenvalues of the Dirichlet Laplacian in bounded perforated …

We provide a full series expansion of a generalization of the so-called u-capacity related to
the Dirichlet–Laplacian in dimension three and higher, extending the results of Abatangelo …

In contrast with the well-known methods of matching asymptotics and multiscale (or
compound) asymptotics, the “functional analytic approach” of Lanza de Cristoforis (Analysis …

We investigate the behavior of the solution of a mixed problem in a domain with two
moderately close holes. We introduce a positive parameter ε and we define a perforated …

This paper concerns the asymptotic expansion of the solution of the Dirichlet–Laplace
problem in a domain with small inclusions. This problem is well understood for the Neumann …

The modeling challenges arising when the problem domain has small supported holes in it
are considered through a representative membrane problem. Such problems are sometimes …

In this paper we study the asymptotic behavior of u-capacities of small sets and its
application to the analysis of the eigenvalues of the Dirichlet-Laplacian on a bounded planar …

We study the Dirichlet problem in a domain with a small hole close to the boundary. To do
so, for each pair ε=(ε 1, ε 2) of positive parameters, we consider a perforated domain Ω ε …