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

Barton, Ariel; Mayboroda, Svitlana

Softcover

ISBN 10: 1470419890 ISBN 13: 9781470419899

Publisher: American Mathematical Society, 2016

Synopsis

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.

About this title

About the Author

Ariel Barton, University of Arkansas, Fayetteville, USA.

Svitlana Mayboroda, University of Minnesota, Minneapolis, USA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2016
• ISBN 10: 1470419890
• ISBN 13: 9781470419899
• Binding: Paperback
• Language: English
• Number of pages: 110