About this Book

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 Lp classes. The authors establish:

(1) Mapping properties for the double and single layer potentials, as well as the Newton potential;

(2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces;

(3) Well-posedness for the non-homogeneous boundary value problems.

In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.