Layer potentials and boundary-value problems for second order elliptic operators with data in Besov spaces

Ariel Barton, Svitlana Mayboroda

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

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

Original languageEnglish (US)
Pages (from-to)1-122
Number of pages122
JournalMemoirs of the American Mathematical Society
Volume243
Issue number1149
DOIs
StatePublished - Sep 2016

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