10 papers · 1 filter
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…
The Fractional-Logarithmic Laplacian: Potentials, Regularity, and Critical Compact Embeddings
Rui Chen
We develop potential-theoretic and \(L^p\)-regularity results for the fractional--logarithmic Laplacian \((-Î)^{s+\ln}\) and its inhomogeneous counterpart \((λI-Î)^{s+\ln}\), \(…
Nonlocal Characterizations of Stochastic Completeness on Complete Riemannian Manifolds
Rui Chen, Bobo Hua
In this paper, we first prove that the following generalized conservation principle holds on complete Riemannian manifolds: for every \(0<s<1\) and \(t>0\), \[ T_t^{(s)}\mathbf 1+\…
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…
On Poincaré-Sobolev level involving fractional GJMS operators on hyperbolic space
Huyuan Chen, Rui Chen
This paper is devoted to a qualitative analysis of the Poincaré--Sobolev level associated with the fractional GJMS operators \(\mathcal{P}_s\) \(\bigl(s\in(0,\tfrac n2)\setminus\ma…