9 citations · 29 across the 25 of their papers we have counts for
19 papers · 1 filter
Double phase anisotropic variational problems involving critical growth
Ky Ho, Yun-Ho Kim, Chao Zhang
In this paper, we investigate some existence results for double phase anisotropic variational problems involving critical growth. We first establish a Lions type concentration-comp…
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 $$ -{\rm div}(|Du|^{p-2}Du+a(x)|Du|^{q-2}Du)=f(x…
Harnack inequality for the nonlocal equations with general growth
Yuzhou Fang, Chao Zhang
We consider a class of generalized nonlocal -Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solut…
Hölder regularity for mixed local and nonlocal -Laplace parabolic equations
Bin Shang, Chao Zhang
We give a unified proof of Hölder regularity of weak solutions for mixed local and nonlocal -Laplace type parabolic equations with the full range of exponents . Our…
Regularity theory for mixed local and nonlocal parabolic p-Laplace equations
Bin Shang, Yuzhou Fand, Chao Zhang
We investigate the mixed local and nonlocal parabolic -Laplace equation \begin{align*} \partial_t u(x,t)-Δ_p u(x,t)+\mathcal{L}u(x,t)=0, \end{align*} where is the local $p…
On weak and viscosity solutions of nonlocal double phase equations
Yuzhou Fang, Chao Zhang
We consider the nonlocal double phase equation \begin{align*} \mathrm{P.V.} &\int_{\mathbb{R}^n}|u(x)-u(y)|^{p-2}(u(x)-u(y))K_{sp}(x,y)\,dy\\ &+\mathrm{P.V.} \int_{\mathbb{R}^n} a(…
Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity
Yuzhou Fang, Chao Zhang
We introduce a new class of quasi-linear parabolic equations involving nonhomogeneous degeneracy or/and singularity $$ \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…
Gaussian Estimates for Heat Kernels of Higher Order Schrödinger Operators with Potentials in Generalized Schechter Classes
Jun Cao, Yu Liu, Dachun Yang +1
Let , be a -order homogeneous elliptic operator with real constant coefficients on , and a measurable functi…
Hypocoercivity and global hypoellipticity for the kinetic Fokker-Planck equation in spaces
Chaoen Zhang
The purpose of this paper is to extend the hypocoercivity results for the kinetic Fokker-Planck equation in space in Villani's memoir \cite{Villani} to higher order Sobolev s…
The boundedness and Hölder continuity of weak solutions to elliptic equations involving variable exponents and critical growth
Ky Ho, Yun-Ho Kim, Patrick Winkert +1
In this paper we prove the boundedness and Hölder continuity of quasilinear elliptic problems involving variable exponents for a homogeneous Dirichlet and a nonhomogeneous Neumann…
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…
The Kinetic Fokker-planck Equation With Mean Field Interaction
Arnaud Guillin, Wei Liu, Liming Wu +1
We study the long time behaviour of the kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fkker-Planck equation. We prove a uniform (in…
Renormalized and entropy solutions for the fractional p-Laplacian parabolic equation with L^1 data
Kaimin Teng, Chao Zhang, Shulin Zhou
In this paper we introduce a natural function class and prove the existence and uniqueness of both nonnegative renormalized solutions and entropy solutions for the fractional p-Lap…
Renormalized solutions for the fractional p(x)-Laplacian equation with L^1 data
Chao Zhang, Xia Zhang
In this paper, we prove the existence and uniqueness of nonnegative renormalized solutions for the fractional p(x)-Laplacian problem with L1 data. Our results are new even in the c…
Harnack's inequality for fractional nonlocal equations
P. R. Stinga, Chao Zhang
We prove interior Harnack's inequalities for solutions of fractional nonlocal equations. Our examples include fractional powers of divergence form elliptic operators with potential…
Regularity estimates in Hölder spaces for Schrödinger operators via a T1 theorem
Tao Ma, P. R. Stinga, J. L. Torrea +1
We derive Hölder regularity estimates for operators associated with a time independent Schrödinger operator of the form . The results are obtained by checking a certain condi…
Regularity properties of Schrödinger operators
Tao Ma, P. R. Stinga, J. L. Torrea +1
Let L be a Schrödinger operator of the form L=-Δ+V, where the nonnegative potential V satisfies a reverse Hölder inequality. Using the method of L-harmonic extensions we study regu…