5 citations · 8 across the 18 of their papers we have counts for
18 papers
Harnack-type estimates for nonlocal double phase functionals
Yuzhou Fang, Chao Zhang
We establish Harnack-type inequalities for local minimizers of nonlocal double phase functionals, involving an explicit two-radius positive-part tail and a negative far-field tail.…
Gradient regularity for nonlocal double phase equations
Yuzhou Fang, Chao Zhang
This paper is devoted to investigating the interior regularity of viscosity solutions to the nonlocal double phase equations $$ \int_{\mathbb{R}^d} \left(\frac{|u(x)-u(y…
Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term
Yuzhou Fang, Juha Kinnunen, Chao Zhang
We investigate a class of degenerate fully nonlinear nonlocal elliptic equations with Hamiltonian terms. By precisely characterizing the interaction between the degeneracy law of e…
Higher Sobolev regularity for mixed local and nonlocal equations with nonstandard growth
Yuzhou Fang, Dingding Li, Chao Zhang
We develop a systematic study of the interior Sobolev regularity of weak solutions to the mixed local and nonlocal -Laplace equations, which model the superposition of two s…
Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations
Yuzhou Fang, Vicentiu D. Radulescu, Chao Zhang
We consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation argumen…
Quantitative analysis and its applications for Keller-Segel type systems
Mengyao Ding, Yuzhou Fang, Chao Zhang
In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented h…
On the weak Harnack inequalities for nonlocal double phase problems
Yuzhou Fang, Chao Zhang
This paper is devoted to studying the weak Harnack inequalities for nonlocal double phase functionals by using expansion of positivity, whose prototype is $$ \iint_{\mathbb{R}^n\ti…
Regularity theory for nonlocal equations with general growth in the Heisenberg group
Yuzhou Fang, Chao Zhang
We deal with a wide class of generalized nonlocal -Laplace equations, so-called nonlocal -Laplace equations, in the Heisenberg framework. Under natural hypotheses on the -…
Local regularity for nonlocal double phase equations in the Heisenberg group
Yuzhou Fang, Chao Zhang, Junli Zhang
We prove interior boundedness and Hölder continuity for the weak solutions of nonlocal double phase equations in the Heisenberg group . This solves a problem raised b…
Local behaviour of the mixed local and nonlocal problems with nonstandard growth
Mengyao Ding, Yuzhou Fang, Chao Zhang
We consider the mixed local and nonlocal functionals with nonstandard growth \begin{eqnarray*} u\mapsto\int_Ω(|Du|^p-f(x)u)\,dx+\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}\frac{|u(x)-u(…
Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation
Yuzhou Fang, Vicentiu D. Radulescu, Chao Zhang
We establish the equivalence between weak and viscosity solutions to the nonhomogeneous double phase equation with lower-order term $$ -{\rm div}(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du)=f(x…
Harnack inequality for the nonlocal equations with general growth
Yuzhou Fang, Chao Zhang
We consider a class of generalized nonlocal -Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solut…
Regularity theory for mixed local and nonlocal parabolic p-Laplace equations
Bin Shang, Yuzhou Fand, Chao Zhang
We investigate the mixed local and nonlocal parabolic -Laplace equation \begin{align*} \partial_t u(x,t)-Δ_p u(x,t)+\mathcal{L}u(x,t)=0, \end{align*} where is the local $p…
On weak and viscosity solutions of nonlocal double phase equations
Yuzhou Fang, Chao Zhang
We consider the nonlocal double phase equation \begin{align*} \mathrm{P.V.} &\int_{\mathbb{R}^n}|u(x)-u(y)|^{p-2}(u(x)-u(y))K_{sp}(x,y)\,dy\\ &+\mathrm{P.V.} \int_{\mathbb{R}^n} a(…
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity
Yuzhou Fang, Chao Zhang
We introduce a new class of quasi-linear parabolic equations involving nonhomogeneous degeneracy or/and singularity $$ \partial_t u=[|D u|^q+a(x,t)|D u|^s]\left(Δu+(p-2)\left\langl…
Regularity of solutions to degenerate fully nonlinear elliptic equations with variable exponent
Yuzhou Fang, Vicentiu D. Radulescu, Chao Zhang
We consider the fully nonlinear equation with variable-exponent double phase type degeneracies Under some appropriate assum…
Gradient Holder regularity for parabolic normalized p(x,t)-Laplace equation
Yuzhou Fang, Chao Zhang
We consider interior Hölder regularity of the spatial gradient of viscosity solutions to the normalized -Laplace equation $$ u_t=\left(δ_{ij}+(p(x,t)-2)\frac{u_i u_j}{|Du|^…
Equivalence between distributional and viscosity solutions for the double-phase equation
Yuzhou Fang, Chao Zhang
We investigate the different notions of solutions to the double-phase equation $$ -\dive(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du)=0, $$ which is characterized by the fact that both elliptici…