5 papers
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…
Sobolev regularity for the perturbed fractional 1-Laplace equations in the subquadratic case
Dingding Li, Chao Zhang
This work investigates the Sobolev regularity of solutions to perturbed fractional 1-Laplace equations. Under the assumption that weak solutions are locally bounded, we establish t…
Sobolev regularity for the nonlocal -Laplace equations in the superquadratic case
Dingding Li, Chao Zhang
We investigate the interior Sobolev regularity of weak solutions to the nonlocal -Laplace equations in the superquadratic case . As a product, the explicit Hölder c…
On equivalence of weak and viscosity solutions to nonlocal double phase problems with nonhomogeneous data
Sekhar Ghosh, R. Lakshmi, Chao Zhang
This work focuses on the nonhomogeneous nonlocal double phase problem \begin{align*} L_au(x)=f(x,u,D_s^p u, D_{a,t}^q u) \text{ in } Ω, \end{align*} where is…
Asymptotic mean value properties for the elliptic and parabolic double phase equations
Weili Meng, Chao Zhang
We characterize an asymptotic mean value formula in the viscosity sense for the double phase elliptic equation $$ -{\rm div}(\lvert \nabla u \rvert^{p-2}\nabla u+ a(x)\lvert\nabla…