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 consider a nonlinear integral operator which involves a Nemytskij type operator and
which appears in the applications as a pull-back of layer potential operators. We prove an …

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 …

Let A(ϵ) be the annular domain obtained by removing from a bounded open domain I^o of ℝ
na small cavity of size ϵ> 0. Then we assume that for some natural index l, lI^o>0 is a simple …

Let Ω be a sufficiently regular bounded connected open subset of such that 0∈ Ω and that is
connected. Then we take q11,…, qnn∈] 0,+∞[and. If ε is a small positive number, then we …

This paper is divided into three parts. The first part focuses on periodic layer heat potentials,
demonstrating their smooth dependence on regular perturbations of the support of …

In this paper we study the existence of solutions in parabolic Schauder space of a nonlinear
mixed boundary value problem for the heat equation in a perforated domain. From a given …

We consider the heat equation in a domain that has a hole in its interior. We impose a
Neumann condition on the exterior boundary and a nonlinear Robin condition on the …

The purpose of this paper is to construct a family of fundamental solutions for elliptic partial
differential operators with quaternion constant coefficients. The elements of such family are …

We consider the acoustic field scattered by a bounded impenetrable obstacle and we study
its dependence upon a certain set of parameters. As usual, the problem is modeled by an …