English

Note on Regularity theory for Nonlinear elliptic equations

Analysis of PDEs 2025-12-16 v3 Differential Geometry

Abstract

In this note, we present several seminal developments in the regularity theory of nonlinear (uniformly) elliptic equations, including the De Giorgi-Nash-Moser theory concerning the Hilbert 19th problem and variational equations, as well as the Krylov-Safonov and Evans-Safonov theories for fully nonlinear equations.

Keywords

Cite

@article{arxiv.2512.03012,
  title  = {Note on Regularity theory for Nonlinear elliptic equations},
  author = {Zhenye Qian},
  journal= {arXiv preprint arXiv:2512.03012},
  year   = {2025}
}

Comments

44 pages, 14 figures

R2 v1 2026-07-01T08:06:08.718Z