3 papers
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.AP2025
Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term
Yuzhou Fang, Juha Kinnunen, Chao Zhang
We investigate a class of degenerate fully nonlinear nonlocal elliptic equations with Hamiltonian terms. By precisely characterizing the interaction between the degeneracy law of e…
math.AP2025
Higher Sobolev regularity for mixed local and nonlocal equations with nonstandard growth
Yuzhou Fang, Dingding Li, Chao Zhang
We develop a systematic study of the interior Sobolev regularity of weak solutions to the mixed local and nonlocal -Laplace equations, which model the superposition of two s…