论文标题
Harnack的不平等和室内规律性，用于Markov流程，具有退化跳跃内核
Harnack inequality and interior regularity for Markov processes with degenerate jump kernels
论文作者
论文摘要
在本文中，我们研究了适当的开放子集中纯粹不连续的马尔可夫进程的内部潜在理论特性$ d \ subset \ mathbb {r}^d $。由于它们可能在边界上消失或炸毁的意义，因此过程的跳跃内核可以在边界处退化。在跳跃内核上的某些自然条件下，我们表明规模不变的harnack不等式适用于任何适当的开放子集$ d \ subset \ mathbb {r}^d $，并证明谐波功能的内部规律性。我们还证明了Dynkin型公式和其他几个内部结果。
In this paper we study interior potential-theoretic properties of purely discontinuous Markov processes in proper open subsets $D\subset \mathbb{R}^d$. The jump kernels of the processes may be degenerate at the boundary in the sense that they may vanish or blow up at the boundary. Under certain natural conditions on the jump kernel, we show that the scale invariant Harnack inequality holds for any proper open subset $D\subset \mathbb{R}^d$ and prove some interior regularity of harmonic functions. We also prove a Dynkin-type formula and several other interior results.
