Linhan Li

Brown University

Talk Title: A_{\infty} condition for elliptic operators with BMO antisymmetric part

Abstract: We investigate the L^p Dirichlet problem for divergence-form operators with an L^{\infty} elliptic symmetric part and a BMO antisymmetric part. These operators are relevant to the study of incompressible flows. We are able to extend, to these operators, various criteria for determining mutual absolute continuity of elliptic measure with surface measure, or, the A_{\infty} condition, in Lipschitz domains. The A_{\infty} condition implies that the L^p Dirichlet problem is solvable for sufficiently large p. Moreover, if we assume additionally that the coefficients of these operators are independent of the vertical variable t in the upper half space, we can obtain the A_{\infty} condition. This generalizes the work of Hofmann, Kenig, Mayboroda and Pipher in 2015.