6 papers
Spectral bounds and heat kernel upper estimates for Dirichlet forms
Aobo Chen, Zhenyu Yu
We use a Harnack-type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part,…
The spectral characteristics of the Sturm Hamiltonian with eventually periodic type
Jie Cao, Zhenyu Yu
In this paper we consider the spectral characteristics of the Sturm Hamiltonian with eventually periodic type frequencies under large coupling and establish strict inequalities bet…
Nonlinear Dynamical Friction from the Doppler-Shifted Equilibrium Memory Kernel
N. R. Sree Harsha, Zhenyuan Yu, Chuang Ren +2
We present a statistical mechanics framework for modeling equilibrium friction coefficients using the Generalized Langevin Equation (GLE). We show that the kernel, obtained via the…
Elliptic Harnack inequalities for mixed local and nonlocal -energy form on metric measure spaces
Aobo Chen, Zhenyu Yu
In the context of metric measure spaces, we introduce an axiomatic formulation of mixed local and nonlocal -energy forms. Within this framework, we use the Poincaré inequality,…
Isolated singularities for elliptic equations with convolution terms in a punctured ball
Marius Ghergu, Zhe Yu
The purpose of this article is two-fold. First, we investigate the inequality $$ -Îu+V(x) u\geq f\quad\mbox{ in } B_1\setminus\{0\}\subset \mathbb{R}^N , N \geq 2, $$ where $f\in…
Non-homogeneous fourth order elliptic inequalities with the convolution term
Zhe Yu
We are concerned with the study of the twin non-local inequalities featuring non-homogeneous differential operators $$\displaystyle -Î^2 u + λÎu \geq (K_{α, β} * u^p)u^q \quad…