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math.AP2026
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,…
math.AP2025
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…
math.AP2024
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…