Hongjie Dong, Brown University

Nonstandard Calderon-Zygmund type estimates for elliptic and parabolic equations

The Lp-theory of elliptic and parabolic equations with discontinuous coefficients has been studied extensively in the last fifty years. On one hand, in view of the well-known counterexamples there does not exist a solvability theory for uniformly elliptic operators with bounded and measurable coefficients. On the other hand, by a result of Jerison and Kenig, even the Poisson equation on a Lipschitz domain may not be solvable in W^1_p for large p unless the boundary is sufficiently flat. Therefore, many efforts have been made to treat particular types of discontinuous coefficients and nonsmooth domains. In this talk, I will review some recent work in this direction.