Square Functions and the \(A_\infty\) Property of Elliptic Measures

In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal Carleson measure estimate for bounded solutions of such operators...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Kenig, C, Kirchheim, B, Pipher, J, Toro, T
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.09.2014
Subjects
Dirichlet problem
Divergence
Domains
Operators
Online AccessGet full text

Cover

More Information
Summary:In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal Carleson measure estimate for bounded solutions of such operators implies a regularity result for the associated elliptic measure.
ISSN:2331-8422