论文标题
莱维型运营商的基本解决方案的规律性
Regularity of fundamental solutions for Lévy-type operators
论文作者
论文摘要
对于一类非对称的非本地lévy-type运算符$ \ mathcal {l}^κ$，其中包括$ \ Mathcal {l}^κF（x）的表格的范围：= \ int _ {\ int _ {\ intbb {\ mathb {r}^d}^d}^d}^d}（f（x+z）（x+z）-f（x+z） - x | \ left <z，\ nabla f（x）\ right>）κ（x，z）j（z）\，dz \ ,, $$我们证明了基本解决方案$ p^κ$的规律性，对等式$ \ partial_t = \ dartial_t = \ mathcal {l}^κ$。
For a class of non-symmetric non-local Lévy-type operators $\mathcal{L}^κ$, which include those of the form $$ \mathcal{L}^κf(x):= \int_{\mathbb{R}^d}( f(x+z)-f(x)- 1_{|z|<1} \left<z,\nabla f(x)\right>)κ(x,z)J(z)\, dz\,, $$ we prove regularity of the fundamental solution $p^κ$ to the equation $\partial_t =\mathcal{L}^κ$.
