Sharp gradient estimates for a class of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions and Hamiltonian terms

Wentao Huo

Sharp gradient estimates for a class of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions and Hamiltonian terms

Analysis of PDEs 2026-07-24 v1

Authors: Wentao Huo

Abstract

This paper focus on a class of singular or degenerate fully nonlinear elliptic equations with Hamiltonian terms under oblique boundary conditions on $C^{1}$ domains. Under quite general conditions on the singularity/degeneracy of the model, we establish the sharp $C^{1,\alpha}$ regularity up to the boundary within a unified framework.

Keywords

singular/degenerate elliptic equation fully nonlinear elliptic equation oblique boundary condition Hamiltonian term sharp gradient estimate boundary regularity

Cite

@article{arxiv.2607.22025,
  title  = {Sharp gradient estimates for a class of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions and Hamiltonian terms},
  author = {Wentao Huo},
  journal= {arXiv preprint arXiv:2607.22025},
  year   = {2026}
}