On C1, C2, and weak type-(1,1) estimates for linear elliptic operators

Hongjie Dong, Seick Kim

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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 languageEnglish
Pages (from-to)417-435
Number of pages19
JournalCommunications in Partial Differential Equations
Volume42
Issue number3
DOIs
Publication statusPublished - 2017 Mar 4

Bibliographical note

Publisher Copyright:
© 2017 Taylor & Francis.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'On C<sup>1</sup>, C<sup>2</sup>, and weak type-(1,1) estimates for linear elliptic operators'. Together they form a unique fingerprint.

Cite this