Analysis Seminar: Dirichlet solvability for elliptic equations, with a singular drift that satisfies a Carleson measure condition
Abstract: We establish the solvability of the Lp Dirichlet problem, for divergence form elliptic equations with a drift that is bounded by the inverse distance to the boundary, in a broad classes of domains, with a natural Carleson measure condition on the drift as considered earlier by Hofmann-Lewis and Kenig-Pipher.
In proving this result, we establish doubling of the elliptic measure corresponding to the operator but with the drift being pointwise bounded by the inverse distance to the boundary with a sufficiently small constant factor, in the absence of any Carleson measure condition.
This is joint work with Prof Steve Hofmann. Time permitting, we will also briefly review a couple of closely related new results on pointwise bounds of Green's functions for elliptic operators with drifts.
Host: Brett Wick