论文标题
一类混合进化方程的热核
Heat kernels for a class of hybrid evolution equations
论文作者
论文摘要
本文的目的是构建（显式）热核，以在物理，保形几何形状和下层PDE中出现的某些混合进化方程。 Hybrid意味着相关的部分差分运算符以$ \ Mathscr L_1 + \ Mathscr L_2- \ partial_t $的形式出现，但是变量无法解耦。结果，无法获得相对热内核作为操作员的热核的产物，$ \ mathscr l_1- \ partial_t $和$ \ Mathscr l_2- \ partial_t $。我们的方法是新的，最终取决于普通的Ornstein-Uhlenbeck经营者，在Hörmander1967年发表的有关低纤维化的开头。
The aim of this paper is to construct (explicit) heat kernels for some hybrid evolution equations which arise in physics, conformal geometry and subelliptic PDEs. Hybrid means that the relevant partial differential operator appears in the form $\mathscr L_1 + \mathscr L_2 - \partial_t$, but the variables cannot be decoupled. As a consequence, the relative heat kernel cannot be obtained as the product of the heat kernels of the operators $\mathscr L_1 - \partial_t$ and $\mathscr L_2 - \partial_t$. Our approach is new and ultimately rests on the generalised Ornstein-Uhlenbeck operators in the opening of Hörmander's 1967 groundbreaking paper on hypoellipticity.
