AI 中文总结
本文研究混合局部-非局部算子 $-\Delta+(-\Delta)^s$ 的基本解，推导其渐近展开并应用于建立相关定理与极大值原理。
AI 中文摘要
本文研究混合局部-非局部算子 $-\Delta+(-\Delta)^s$（$0<s<1$）的基本解，推导其基本解及其梯度的精确渐近展开，包含首个非平凡修正项，覆盖原点附近与无穷远处，描述局部与非局部扩散尺度间的过渡，含出现对数项的临界情形。作为该渐近的应用，建立孤立奇点非负超解的分布型Bôcher型定理，进一步得到穿孔球上的定量正与反对称极大值原理。
英文摘要
In this paper, we study the fundamental solution of the mixed local-nonlocal operator $ -Δ+(-Δ)^s,$ $ 0<s<1. $ We derive precise asymptotic expansions of the fundamental solution and its gradient, up to the first nontrivial correction term, both near the origin and at infinity. The expansions describe the transition between the local and nonlocal diffusion scales and include the critical regimes in which logarithmic terms occur. As applications of these asymptotics, we establish a distributional Bôcher-type theorem for nonnegative supersolutions with an isolated singularity. We further obtain quantitative positive and antisymmetric maximum principles on punctured balls.
Comments28 pages; comments and suggestions are welcome
