9 citations · 17 across the 15 of their papers we have counts for
19 papers
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 $$ -{\rm div}(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du)=f(x…
Boundedness of differential transforms for Poisson semigroups generated by Bessel operators
Chao Zhang
In this paper we analyze the convergence of the following type of series \begin{equation*} T_N f(x)=\sum_{j=N_1}^{N_2} v_j\Big(\mathcal{P}_{a_{j+1}} f(x)-\mathcal{P}_{a_{j}} f(x)\B…
Harnack inequality for the nonlocal equations with general growth
Yuzhou Fang, Chao Zhang
We consider a class of generalized nonlocal -Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solut…
Regularity theory for mixed local and nonlocal parabolic p-Laplace equations
Bin Shang, Yuzhou Fand, Chao Zhang
We investigate the mixed local and nonlocal parabolic -Laplace equation \begin{align*} \partial_t u(x,t)-Δ_p u(x,t)+\mathcal{L}u(x,t)=0, \end{align*} where is the local $p…
On weak and viscosity solutions of nonlocal double phase equations
Yuzhou Fang, Chao Zhang
We consider the nonlocal double phase equation \begin{align*} \mathrm{P.V.} &\int_{\mathbb{R}^n}|u(x)-u(y)|^{p-2}(u(x)-u(y))K_{sp}(x,y)\,dy\\ &+\mathrm{P.V.} \int_{\mathbb{R}^n} a(…
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity
Yuzhou Fang, Chao Zhang
We introduce a new class of quasi-linear parabolic equations involving nonhomogeneous degeneracy or/and singularity $$ \partial_t u=[|D u|^q+a(x,t)|D u|^s]\left(Δu+(p-2)\left\langl…