The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

In Chapter 1 we presented basic ideas for the reduction of boundary value problems of the
Laplacian to various forms of boundary integral equations based on the direct approach …

We study tangential vector fields on the boundary of a bounded Lipschitz domain Ω in R 3.
Our attention is focused on the definition of suitable Hilbert spaces corresponding to …

The first two chapters contain introductory courses. Chapter 1 presents the theory of Sobolev-
type spaces Hs (s∈ R) on Rn, on a smooth closed manifold, and on a smooth bounded …

We study inhomogeneous boundary value problems for the Laplacian in arbitrary Lipschitz
domains with data in Sobolev–Besov spaces. As such, this is a natural continuation of work …

In this paper we provide a mathematical framework for localized plasmon resonance of
nanoparticles. Using layer potential techniques associated with the full Maxwell equations …

In a three-dimensional bounded possibly multiply connected domain, we give gradient and
higher-order estimates of vector fields via div and curl in Lp-theory. Then, we prove the …

Variational boundary integral equations for Maxwell's equations on Lipschitz surfaces in
\mathbbR^3 are derived and their well-posedness in the appropriate trace spaces is …

We extend to the variable coefficient case boundary layer techniques that have been
successful in the treatment of the Laplace equation and certain other constant coefficient …

Spectral boundary-value problems with discrete spectrum are considered for second-order
strongly elliptic systems of partial differential equations in a domain whose boundary is …