UNIFORM C1,1 ESTIMATES OF HOMOGENIZATION OF ELLIPTIC EQUATIONS IN NON-DIVERGENCE FORM WITH DINI CONDITIONS

The paper is concerned with regularity of elliptic equations in non-divergence form with homogenization. We establish uniform interior and boundary C-1,C-1 estimates in bounded C-2,C-Dini domains provided the coefficients and inhomogeneous terms of equations are Dini continuous and the boundary data are of C-2,C-Dini, which weakens the assumptions of some existence results.

Automated summary

The paper discusses the regularity of elliptic equations in non-divergence form with homogenization. We establish uniform interior and boundary C-1,C-1 estimates in bounded C-2,C-Dini domains, provided that the coefficients and inhomogeneous terms of the equations are Dini continuous, and the boundary data are of C-2,C-Dini, which weakens the assumptions of some existence results.