On $C^1$, $C^2$, and weak type-$(1,1)$ estimates for linear elliptic operators
Analysis of PDEs
2017-10-13 v3
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 -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 Brezis. We also prove a weak type- estimate under a stronger assumption on the modulus of continuity. The corresponding results for non-divergence form equations are also established.
Cite
@article{arxiv.1607.04361,
title = {On $C^1$, $C^2$, and weak type-$(1,1)$ estimates for linear elliptic operators},
author = {Hongjie Dong and Seick Kim},
journal= {arXiv preprint arXiv:1607.04361},
year = {2017}
}
Comments
17 pages; accepted in Communications in Partial Differential Equations; minor changes in text