Author

Xue-Mei Li

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Preprint Sep 2026

Boundary pointwise regularity for the $p$-Laplace equation on $C^{1,\mathrm{Dini}}$ domains

This paper investigates the boundary pointwise regularity of solutions to the p-Laplace equation. By treating curved boundaries as perturbations of flat ones, we establish the boundary pointwise Lipschitz regularity under the exterior $C^{1,\mathrm{Dini}}$ condition and the Hopf lemma under the interior $C^{1,\mathrm{D...

Xue-Mei Li, Yuan-Yuan Lian · 0 citations

Preprint Sep 2026

Boundary Regularity for Fully Nonlinear Singular Elliptic Equations

We study boundary regularity for the fully nonlinear singular elliptic equation of the form $|Du|^\gamma F(D^2u)=f$, where $-1<\gamma<0$. First, we prove pointwise boundary $C^{1,\alpha}$ estimates with pointwise $C^{1,\alpha}$ Dirichlet data, which weakens the $C^2$ domain smoothness requirement from Birindelli and De...

Ji-Qing Dong, Xue-Mei Li · 0 citations