Weighted analyticity of Hartree-Fock eigenfunctions

TL;DR

This paper establishes weighted analyticity estimates for Hartree-Fock eigenfunctions near singularities, enhancing understanding of their regularity and aiding numerical approximation methods.

Contribution

It extends classical analyticity results by providing weighted estimates at singular points for Hartree-Fock eigenfunctions, with implications for numerical analysis.

Findings

Weighted estimates at singular points with derivatives control

Implications for a priori numerical solution estimates

Extension of classical analyticity results

Abstract

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.