| Abstract: |
In this talk, we shall show the well-posedness of $L^p$ Dirichlet problem on the upper-half space for elliptic operators with non-smooth coefficients that have a BMO antisymmetric part. In particular, the coefficients of the operator are not necessarily bounded. Our method relies on kernel estimates and off-diagonal estimates for the semigourp $e^{-tL}$, solution to the Kato problem, and various estimates for the Hardy norms of certain commutators. This is based on joint work with S. Hofmann, S. Mayboroda, and J. Pipher. |
