Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces (eBook)

Ariel Barton (Autor)

eBook Download: PDF

2016
110 Seiten
American Mathematical Society (Verlag)
978-1-4704-3446-5 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 8.2.2016
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• ISBN-10: 1-4704-3446-6 / 1470434466
• ISBN-13: 978-1-4704-3446-5 / 9781470434465