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 derive the equation of a free vibrating thin plate whose mass is concentrated at the
boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard …

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 …

We investigate the effective thermal conductivity of a two-phase composite with thermal
resistance at the interface. The composite is obtained by introducing into an infinite …

Let be a bounded open domain of. Let denote the outward unit normal of. We assume that
the Steklov problem Δu= 0 in and on has a simple eigenvalue of. Then we consider an …

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 …

We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a
real parameter ϵ and we denote by u ϵ the corresponding solution. The behavior of u ϵ for …

We consider a heat transmission problem for a composite material which fills the n-
dimensional Euclidean space. The composite has a periodic structure and consists of two …