Green's function for nondivergence elliptic operators in two dimensions

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. We show that the Green's function is BMO in the domain and establish logarithmic pointwise bounds. We also obtain pointwise bounds for first and second derivatives of the Green's function.

20 pages

References in corpus (2)

• The Green function estimates for strongly elliptic systems of second order
• Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains

Cited by in corpus (5)

• Learning elliptic partial differential equations with randomized linear algebra
• The Dirichlet problem for second-order elliptic equations in non-divergence form with continuous coefficients
• Homogenization Theory of Elliptic System with Lower Order Terms for Dimension Two
• 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