Author

Chao Zhang

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Preprint Aug 2026

Gradient H\"older regularity for singular fractional $p$-Laplace equations

Let $n\ge2$, $1p-1$. We prove that every globally bounded fractional $p$-harmonic function is locally $C^{1,\alpha}$ for some $\alpha=\alpha(n,p,s)>0$. This settles the open problem of interior gradient H\"older regularity in the singular range throughout the natural first-order regime $sp>p-1$. The proof combines an a...

Chao Zhang · 0 citations

Preprint Aug 2026

Gradient regularity and potential estimates for fractional drift--diffusion equations in the critical and subcritical ranges

We establish scale-invariant interior $C^{1,\alpha}$ estimates for bounded viscosity solutions of $(-\Delta)^su+b\cdot\nabla u=f$ for $s\in[1/2,1)$ with locally H\"older $b$ and $f$. The critical case uses Silvestre's parabolic theorem; the subcritical case uses Schauder estimates and interpolation. Applying this visco...

Qi Xue, Chao Zhang · 0 citations