On C1, C2, and weak type-(1, 1) estimates for linear elliptic operators. Issue 3 (4th March 2017) - Dong, Hongjie; Kim, Seick
ABSTRACT: We show that any weak solution to elliptic equations in divergence form is continuously differentiable provided that the modulus of continuity of coefficients in the L 1 -mean sense satisfies the Dini condition. This in particular answers a question recently raised by Yanyan Li and allows us to improve a result of Haïm Brezis. We also prove a weak type-(1, 1) estimate under a stronger assumption on the modulus of continuity. The corresponding results for nondivergence form equations are also established.