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We investigate the regularity of elliptic equations in double divergenceform, with leading coefficients satisfying the Dini mean oscillation condition.We prove that the solutions are differentiable on the zero level set and derivea pointwise bound for the derivative. As an application, we establish globalpointwise estimates for the Green's function of second-order uniformly ellipticoperators in non-divergence form, considering Dini mean oscillationcoefficients in bounded $C^{1,1}$ domains.

Regularity of elliptic equations in double divergence form and applications to Green's function estimates