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

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  • Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces Book Detail

  • Author : Ariel Barton:
  • Release Date : 2016-09-06
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 122
  • ISBN 13 : 1470419890
  • File Size : 3,3 MB
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Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces by Ariel Barton: PDF Summary

Book Description: 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.

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