13 papers
Sharp constants in the one-sided John-Nirenberg inequality for functions of bounded lower oscillation
Chao Zhang
We determine the sharp constants in the one-sided John-Nirenberg inequality for functions of bounded lower oscillation on an interval. More precisely, if $f\in\BLO(I_0)$, then $$ \…
Noncommutative maximal differential transforms associated to averaging operators
Shaohong Liang, Yu Wang, Bang Xu +1
In this paper, we establish the noncommutative maximal weak type and strong type estimates for the family of operators , defined by $$T_Nf=\sum_{k=N_1}^{N_…
New characterizations of BLO spaces by heat semigroups and applications
Shaohong Liang, Dongyong Yang, Chao Zhang
In this paper, we give two new characterizations of the bounded lower oscillation (BLO) space by using the Gaussian heat semigroup. Using these characterizations, we prove the boun…
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…
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…
Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation
Dingding Li, Chao Zhang
We consider a class of parabolic nonlocal -Laplacian equation \begin{align*} u_t+(-Δ)^s_1u=f \quad \text{ in }Ω\times(0,T]. \end{align*} By employing the Rothe time-discretizati…
Generalized Young Measure Solutions for a Class of Quasilinear Parabolic Equations with Linear Growth
Jingfeng Shao, Zhichang Guo, Chao Zhang
Using the generalized Young measure theory, we extend the theory of Young measure solutions to a class of quasilinear parabolic equations with linear growth, and introduce the conc…
On the weak Harnack inequalities for nonlocal double phase problems
Yuzhou Fang, Chao Zhang
This paper is devoted to studying the weak Harnack inequalities for nonlocal double phase functionals by using expansion of positivity, whose prototype is $$ \iint_{\mathbb{R}^n\ti…
On the solutions of nonlocal 1-Laplacian equation with -data
Dingding Li, Chao Zhang
We study the solutions to a nonlocal 1-Laplacian equation given by $$ 2\text{P.V.}\int_{\mathbb{R}^N}\frac{u(x)-u(y)}{|u(x)-u(y)|} \frac{dy}{|x-y|^{N+s}}=f(x) \quad \textmd{for } x…
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…