Persistence of the Thomas-Fermi approximation for ground states supported by the nonlinear confinement

TL;DR

This paper rigorously justifies the use of the Thomas-Fermi approximation for certain elliptic problems with nonlinear confinement, employing resolvent estimates and fixed-point methods.

Contribution

It provides a mathematical validation of the Thomas-Fermi approximation in the context of nonlinear confinement, bridging a gap between physics and rigorous analysis.

Findings

Validation of the Thomas-Fermi approximation for the specified elliptic problem

Development of resolvent estimates and fixed-point techniques for the analysis

Applicable to models with nonlinear confinement in physical literature

Abstract

We justify the Thomas--Fermi approximation for the elliptic problem with the repulsive nonlinear confinement used in the recent physical literature. The method is based on the resolvent estimates and the fixed-point iterations.