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math.AP2026
Gradient regularity for nonlocal double phase equations
Yuzhou Fang, Chao Zhang
The paper proves that viscosity solutions of a nonlocal double phase equation have Hölder continuous gradients (interior C^{1,α} regularity) under Lipschitz continuity of the modul…
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…