Gradient continuity for $p$-Laplacian obstacle problems under mean oscillation conditions

Sungjin Lee; Jihoon Ok

Gradient continuity for $p$-Laplacian obstacle problems under mean oscillation conditions

Analysis of PDEs 2026-07-08 v1

Authors: Sungjin Lee , Jihoon Ok

Abstract

We establish the $C^1$ -regularity of solutions to the obstacle problems associated with $p$ -Laplacian type equations, where $1<p<\infty$ . Specifically, we prove that the gradient of the solution is continuous under a Dini mean oscillation ( $\mathsf{DMO}$ ) type condition on the data, which includes the coefficient matrix, the source term, and the obstacle function. This result relaxes the classical Dini continuity assumption on the data to a more general mean oscillation condition.

Cite

@article{arxiv.2607.07018,
  title  = {Gradient continuity for $p$-Laplacian obstacle problems under mean oscillation conditions},
  author = {Sungjin Lee and Jihoon Ok},
  journal= {arXiv preprint arXiv:2607.07018},
  year   = {2026}
}