English

Sparse gradient bounds for divergence form elliptic equations

Analysis of PDEs 2024-09-19 v2 Classical Analysis and ODEs

Abstract

We provide sparse estimates for gradients of solutions to divergence form elliptic partial differential equations in terms of the source data. We give a general result of Meyers (or Gehring) type, a result for linear equations with VMO coefficients and a result for linear equations with Dini continuous coefficients. In addition, we provide an abstract theorem conditional on PDE estimates available. The linear results have the full range of weighted estimates with Muckenhoupt weights as a consequence.

Keywords

Cite

@article{arxiv.2402.16213,
  title  = {Sparse gradient bounds for divergence form elliptic equations},
  author = {Olli Saari and Hua-Yang Wang and Yuanhong Wei},
  journal= {arXiv preprint arXiv:2402.16213},
  year   = {2024}
}

Comments

v2: writing improved all over and more details added

R2 v1 2026-06-28T14:59:41.070Z