Green's Function for Nondivergence Elliptic Operators in Two Dimensions
Hongjie Dong, Seick Kim · SIAM Journal on Mathematical Analysis · 2021
We construct the Green function for second-order elliptic equations in nondivergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that Green's function is a bounded mean oscillation in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of Green's function.