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 L1-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.
Original language | English |
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Pages (from-to) | 417-435 |
Number of pages | 19 |
Journal | Communications in Partial Differential Equations |
Volume | 42 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2017 Mar 4 |
Bibliographical note
Publisher Copyright:© 2017 Taylor & Francis.
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics