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Green's Function for Nondivergence Elliptic Operators in Two Dimensions
Hongjie Dong, Seick Kim
Source abstract
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.
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