  This monograph presents a comprehensive treatment of second order divergence
form elliptic operators with bounded measurable t-independent coefficients in
spaces of fractional smoothness, in Besov and weighted Sobolev classes.
  We establish mapping properties for the double and single layer potentials,
as well as the Newton potential, on Besov spaces. We prove extrapolation-type
solvability results: that is, we show that solvability of the Dirichlet or
Neumann boundary value problem at any given L^p space automatically assures
their solvability in an extended range of Besov spaces. We also establish
well-posedness for non-homogeneous boundary value problems.
  In particular, we prove well-posedness of the non-homogeneous Dirichlet
problem with data in Besov spaces for operators with real, not necessarily
symmetric coefficients.

Analysis of PDEs