Chao Zhang

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math.AP2026

Gradient Hölder regularity for singular fractional $p$ -Laplace equations

Chao Zhang

Let $n \geq 2$ , $1 < p < 2$ , $0 < s < 1$ , and $s p > p - 1$ . We prove that every globally bounded fractional $p$ -harmonic function is locally $C^{1, α}$ for some $α = α (n, p, s) > 0$ . This settles the op…

math.AP2026

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

Qi Xue, Chao Zhang

We establish scale-invariant interior $C^{1, α}$ estimates for bounded viscosity solutions of $(- Δ)^{s} u + b \cdot \nabla u = f$ for $s \in [1/2, 1)$ with locally Hölder $b$ and $f$ . The criti…

math.AP2026

Gradient regularity for nonlocal double phase equations

Yuzhou Fang, Chao Zhang

This paper is devoted to investigating the interior $C^{1, α}$ regularity of viscosity solutions to the nonlocal double phase equations $$ \int_{\mathbb{R}^d} \left(\frac{|u(x)-u(y…

math.AP2024

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

Yuzhou Fang, Vicentiu D. Radulescu, Chao Zhang

We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation argumen…

math.AP2024

Quantitative analysis and its applications for Keller-Segel type systems

Mengyao Ding, Yuzhou Fang, Chao Zhang

In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented h…

Gradient Hölder regularity for singular fractional p-Laplace equations

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

Gradient regularity for nonlocal double phase equations

Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

Quantitative analysis and its applications for Keller-Segel type systems

Gradient Hölder regularity for singular fractional $p$ -Laplace equations