论文标题
Hartree-Fock本征函数的加权分析性
Weighted analyticity of Hartree-Fock eigenfunctions
论文作者
论文摘要
我们证明了在一类椭圆形和非线性特征值问题的具有奇异电位的问题的特征函数上的加权Sobolev空间中的分析类型估计值，其中包括Hartree-fock方程。超越了对波形远离细胞核的分析性的经典结果，我们在每个单个点上局部证明了加权估计值，并精确控制了所有顺序的衍生物。 我们的估计值对所考虑的问题的本征函数近似具有深远的影响，并且可以用来证明对此类特征值问题的数值解决方案的先验估计。
We prove analytic-type estimates in weighted Sobolev spaces on the eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with singular potentials, which includes the Hartree-Fock equations. Going beyond classical results on the analyticity of the wavefunctions away from the nuclei, we prove weighted estimates locally at each singular point, with precise control of the derivatives of all orders. Our estimates have far-reaching consequences for the approximation of the eigenfunctions of the problems considered, and they can be used to prove a priori estimates on the numerical solution of such eigenvalue problems.
