A class of nonlocal hypoelliptic operators and their extensions
A class of nonlocal hypoelliptic operators and their extensions
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一类非局部亚椭圆算子及其扩展
DOI：
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发表时间：
2018
影响因子：
1.1
通讯作者：
G. Tralli
中科院分区：
文献类型：
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作者：
N. Garofalo;G. Tralli
本文研究了由次椭圆算子的分数次幂驱动的非局部方程，其形式为$$mathscr Ku=mathscr A u-Partial_t u overset{def}{=}算子名{tr}(Q
Abla^2 u)+-Partial_tu，$$是由H“Ormander在1967年的亚椭圆性论文中引入的。我们证明了非局部算子$(-mathscr K)、S$和$(-mathscr A)、S$可以被实现为双重退化扩张问题的Dirichlet-to-Neumann映射。我们在$L^inty$和$L^p$中解决了这类问题。当$算子名{tr}(B)geq_0$时，我们引入了$。在即将到来的工作中，我们利用这样的演算建立了一些新的Sobolev型和运算不等式。
In this paper we study nonlocal equations driven by the fractional powers of hypoelliptic operators in the form $$mathscr K u = mathscr A u - partial_t u overset{def}{=} operatorname{tr}(Q
abla^2 u) + - partial_t u,$$ introduced by H"ormander in his 1967 hypoellipticity paper. We show that the nonlocal operators $(-mathscr K)^s$ and $(-mathscr A)^s$ can be realized as the Dirichlet-to-Neumann map of doubly-degenerate extension problems. We solve such problems in $L^infty$, and in $L^p$ for $1leq p<infty$ when $operatorname{tr}(B)geq 0$. In forthcoming works we use such calculus to establish some new Sobolev and isoperimetric inequalities.