论文标题
Faber-Krahn的不平等现象的Schrödinger经营者，具有点和库仑相互作用
Faber-Krahn inequalities for Schrödinger operators with point and with Coulomb interactions
论文作者
论文摘要
我们获得了新的Faber-krahn型不平等，以使Dirichlet Laplacian在有限的域上的某些扰动。首先，我们为Schrödinger操作员建立了二维和三维的Faber-Krahn不等式，具有点相互作用：优化者是球的中心支持点相互作用的球。接下来，我们建立了具有吸引人的库仑相互作用的一体和两体Schrödinger操作员的三维Faber-Krahn不平等现象，优化者是根据球中心的库仑吸引力给出的。这种结果的证明是基于对称减少的重排和施泰纳重排技术。在第一个模型中，还需要对最低特征值的某些单调性能进行仔细的分析。
We obtain new Faber-Krahn-type inequalities for certain perturbations of the Dirichlet Laplacian on a bounded domain. First, we establish a two- and three-dimensional Faber-Krahn inequality for the Schrödinger operator with point interaction: the optimiser is the ball with the point interaction supported at its centre. Next, we establish three-dimensional Faber-Krahn inequalities for one- and two-body Schrödinger operator with attractive Coulomb interactions, the optimiser being given in terms of Coulomb attraction at the centre of the ball. The proofs of such results are based on symmetric decreasing rearrangement and Steiner rearrangement techniques; in the first model a careful analysis of certain monotonicity properties of the lowest eigenvalue is also needed.
