12 papers
Sharp Lifespan Dichotomies and Threshold Phenomena for Semilinear Heat Equations Driven by the Logarithmic Laplacian
Huyuan Chen, Rui Chen, Daniel Hauer +1
We study nonnegative mild solutions of \[ \partial_tu+(-Î)^{\ln}u=f(u) \qquad \text{in }(0,T)\times\mathbb R^N, \] with initial datum \(u(0,\cdot)=μu_0\), \(μ>0\). Unlike the cl…
On finite-energy solutions of Kazan-Warner equations on the lattice graph
Huyuan Chen, Bobo hua
We investigate finite-energy solutions to Kazdan-Warner type equations in 2-dimensional integer lattice graph w…
On positive solutions of Lane-Emden equations on the integer lattice graphs
Huyuan Chen, Bobo Hua, Feng Zhou
In this paper, we investigate the existence and nonexistence of positive solutions to the Lane-Emden equations on the -dimensional integer lattice grap…
Maximal hypersurfaces with prescribed light-like cones in Lorentz-Minkowski space
Huyuan Chen, Ying Wang, Feng Zhou
The purpose in this paper is to study the maximal hypersurfaces with multiple light-cones in Lorentz-Minkowski space by considering the weak solutions to the mean curvature equatio…
The Fractional-Logarithmic Laplacian:Fundamental Properties and Eigenvalues
Huyuan Chen, Rui Chen, Daniel Hauer
In this paper, we introduce, for the first time, the fractional--logarithmic Laplacian \( (-Î)^{s+\log} \), defined as the derivative of the fractional Laplacian \( (-Î)^t \) at…
The Conformal Fractional--Logarithmic Laplacian on the Sphere: Yamabe Problems and Sharp Inequalities
Huyuan Chen, Rui Chen, Daniel Hauer
In this paper, we introduce the conformal fractional--logarithmic Laplacian on the unit sphere, defined as the derivative of the conformal fractional Laplacian with respect to the…