Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift
Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift
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DOI：
10.1016/j.jfa.2013.02.011
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发表时间：
2012-07
期刊：
影响因子：
--
通讯作者：
Yasunori Maekawa;Miura Hideyuki
中科院分区：
文献类型：
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作者：
Yasunori Maekawa;Miura Hideyuki
我们考虑一类具有散度自由漂移项的非局部扩散方程，其中扩散算子与某些跳跃型Dirichlet形式有关。在漂移项速度的弱假设下，我们得到了方程基本解的逐点上界。我们的速度类包括具有尺度临界正则性的函数和一些在空间无穷远处的增长函数。
We consider some non-local diffusion equations in the presence of a divergence free drift term, where the diffusion operators are related to certain Dirichlet forms of jump type. We derive pointwise upper bounds for fundamental solutions of the equations under weak assumptions for the velocity of the drift term. Our class of the velocity includes functions with the scale-critical regularity and some growing functions at spatial infinity.