论文标题
对椭圆形的不平等的反示例
Counterexamples to elliptic Harnack inequality for isotropic unimodal Lévy processes
论文作者
论文摘要
到目前为止，每个次级布朗尼运动（SBM）是否满足椭圆形的不平等现象（EHI），这一直是一个悬而未决的问题。 In this paper, we show that the answer is ``no." In our first theorem, we show that if $X=(X_t)_{t \geq 0}$ is an isotropic unimodal Lévy process, and $X$ satisfies certain criteria (involving the jump kernel of $X$ and the distribution of the location upon first exiting balls of various sizes) then $X$ does not satisfy EHI. (Note各向同性的单峰莱维过程大于SBMS类。）然后，我们检查许多特定的SBM确实确实满足了标准，因此不符合EHI。
Until now, it has been an open question whether every subordinated Brownian motion (SBM) satisfies the elliptic Harnack inequality (EHI). In this paper, we show that the answer is ``no." In our first theorem, we show that if $X=(X_t)_{t \geq 0}$ is an isotropic unimodal Lévy process, and $X$ satisfies certain criteria (involving the jump kernel of $X$ and the distribution of the location upon first exiting balls of various sizes) then $X$ does not satisfy EHI. (Note that the class of isotropic unimodal Lévy processes is larger than the class of SBMs.) We then check that many specific SBMs do indeed satisfy the criteria, and thus do not satify EHI.
