论文标题
harnack的不平等和随机反应扩散方程的不平等现象，$ l^p $
Harnack Inequalities and Ergodicity of Stochastic Reaction-Diffusion Equation in $L^p$
论文作者
论文摘要
我们为随机反应 - 扩散方程式提供了Harnack的不平等，其耗散漂移是由$ l^p $ - 空间在任何$ p \ ge 2 $中驱动的。这些不等式用于调查相应的马尔可夫半群$（p_t）$的终点。我们方法的主要成分是通过变更度量来耦合。将我们的结果应用于随机反应扩散方程，超线性生长漂移具有负引导系数，受Lipschitz术语扰动，表明$（p_t）$在所有$ p \ ge 2 $中具有独特的且因此具有$ l^p $的独特且因此具有巨大的不变性，而不是Lipschitz术语。
We derive Harnack inequalities for a stochastic reaction-diffusion equation with dissipative drift driven by additive irregular noise in the $L^p$-space for any $p \ge 2$. These inequalities are utilized to investigate the ergodicity of the corresponding Markov semigroup $(P_t)$. The main ingredient of our method is a coupling by the change of measure. Applying our results to the stochastic reaction-diffusion equation with a super-linear growth drift having a negative leading coefficient, perturbed by a Lipschitz term, indicates that $(P_t)$ possesses a unique and thus ergodic invariant measure in $L^p$ for all $p \ge 2$, which is independent of the Lipschitz term.
