A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations (Q1580854)

This paper was motivated by the study of nonsymmetric elliptic equations. The authors prove two theorems which give sufficient conditions for the elliptic measure of an elliptic divergence form operator to belong to \(A_{\infty}\) (the Muckenhoupt weight class) with respect to the surface measure on the boundary of a Lipschitz domain. The general criterion that this \(A_{\infty}\) condition implies solvability of the \(L^p\) Dirichlet problem for some value of \(p\) which depends on the operator is verified for a class of divergence form nonsymmetric operators.