论文标题
相对论福克 - 普兰克操作员的harnack不平等和渐近下限
Harnack inequality and asymptotic lower bounds for the relativistic Fokker-Planck operator
论文作者
论文摘要
我们在特殊相对论的框架中考虑了二阶退化动力学运算符$ \ mathscr {l} $的类别。我们首先将$ \ Mathscr {l} $描述为Hörmander操作员，相对于Lorentz转换是不变的。然后，我们证明了Lorentz-Invariant Harnack类型不等式，并为$ \ MATHSCR {l} f = 0 $得出准确的渐近下限。结果，我们获得了与$ \ mathscr {l} $相关的相对论随机过程的密度的下限。
We consider a class of second order degenerate kinetic operators $\mathscr{L}$ in the framework of special relativity. We first describe $\mathscr{L}$ as an Hörmander operator which is invariant with respect to Lorentz transformations. Then we prove a Lorentz-invariant Harnack type inequality, and we derive accurate asymptotic lower bounds for positive solutions to $\mathscr{L} f = 0$. As a consequence we obtain a lower bound for the density of the relativistic stochastic process associated to $\mathscr{L}$.
