This book is the first introductory and self-contained presentation of a method for the
analysis of singularly perturbed boundary value problems that we have called the Functional …

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 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 this paper we analyse a boundary value problem for the Laplace equation with a
nonlinear non-autonomous transmission conditions on the boundary of a small inclusion of …

We analyse the spectral convergence of high order elliptic differential operators subject to
singular domain perturbations and homogeneous boundary conditions of intermediate type …

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 …

In this contribution we are interested in the quantitative homogenization properties of linear
elliptic equations with homogeneous Dirichlet boundary data in polygonal domains with …

We consider the Poisson equation with homogeneous Dirichlet conditions in a family of
domains in $ R^{n} $ indexed by a small parameter $\epsilon $. The domains depend on …

We lay down the preliminary work to apply the Functional Analytic Approach to quasi-
periodic boundary value problems for the Helmholtz equation. This consists in introducing a …

For each pair ε=(ε 1, ε 2) of positive parameters, we define a perforated domain Ω ε by
making a small hole of size ε 1 ε 2 in an open regular subset Ω of ℝ n (n≥ 3). The hole is …