BMO Solvability and the A  Condition for Elliptic Operators

Martin Dindos, Carlos Kenig, Jill Pipher

Research output: Contribution to journalArticlepeer-review

Abstract

We establish a connection between the absolute continuity of elliptic measure associated with a second order divergence form operator with bounded measurable coefficients with the solvability of an end-point BMO Dirichlet problem. We show that these two notions are equivalent. As a consequence we obtain an end-point perturbation result, i.e., the solvability of the BMO Dirichlet problem implies L-p solvability for all p > p(0).

Original languageEnglish
Pages (from-to)78-95
Number of pages18
JournalJournal of Geometric Analysis
Volume21
Issue number1
DOIs
Publication statusPublished - Jan 2011

Keywords

  • Dirichlet problem
  • Elliptic measure
  • Bounded mean oscillation
  • WEIGHTED NORM INEQUALITIES
  • DIRICHLET PROBLEM
  • MAXIMAL FUNCTIONS
  • HARDY-SPACES
  • EQUATIONS
  • DOMAINS
  • COEFFICIENTS
  • CONTINUITY
  • VARIABLES

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