On Green's functions of nondivergent elliptic operators with continuous coefficients

It is well known that the elliptic operators in the divergence form admit Green’s functions that are comparable to those of the Laplace operator, even when the coefficients are just measurable.

However, unlike Green’s function for elliptic operators in the divergence form, Green’s function for nondivergence form elliptic operators does not necessarily have pointwise bounds, even if the domain is smooth and the coefficients are uniformly continuous.

In this talk, I will talk about construction and estimates for Green's functions of nondivergent elliptic operators with continuous coefficients satisfying Dini mean oscillation conditions.