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Description of  Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators With Data in Besov Spaces (Memoirs of the American Mathematical Society)

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 $L^p$ 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 $L^p$ 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.