论文标题
Rayleigh-Faber-Krahn，Lyapunov和Hartmann-Wintner不平等现象
Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems
论文作者
论文摘要
在圆柱域中的本文中，我们考虑了具有差异条件的分数椭圆操作员。我们证明，在同一lebesgue度量的所有圆柱域中，在圆柱体中，将分数椭圆算子的第一个特征值最小化。这种不平等被称为雷利·菲尔·克拉恩（Rayleigh-Faber-Krahn）不平等。另外，我们为分数椭圆边界值问题提供Lyapunov和Hartmann-Wintner不平等。
In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operator is minimised in a circular cylinder among all cylindrical domains of the same Lebesgue measure. This inequality is called the Rayleigh-Faber-Krahn inequality. Also, we give Lyapunov and Hartmann-Wintner inequalities for the fractional elliptic boundary value problem.
