Green's function for second order elliptic equations in non-divergence form

Abstract

We construct the Green function for second order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition and the domain has $C^{1,1}$ boundary. We also obtain pointwise bounds for the Green functions and its derivatives.

12 pages

References in corpus (3)

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• On $C^1$, $C^2$, and weak type-$(1,1)$ estimates for linear elliptic operators
• On $C^1$, $C^2$, and weak type-$(1,1)$ estimates for linear elliptic operators: Part II

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• Higher order boundary Harnack principles in Dini type domains
• Note on Green's functions of non-divergence elliptic operators with continuous coefficients
• Regularity of elliptic equations in double divergence form and applications to Green's function estimates
• Refined regularity at critical points for linear elliptic equations