Some a priori estimates for a critical Schrodinger-Newton equation

TL;DR

This paper derives a priori estimates for solutions to a critical Schrödinger-Newton equation, linking quantum mechanics, geometric analysis, and conformal geometry under natural energy and decay conditions.

Contribution

It provides new a priori bounds for a generalized Schrödinger-Newton equation with critical exponent, connecting quantum models with geometric problems.

Findings

Established a priori estimates under energy and decay assumptions

Generalized classical Schrödinger-Newton equations to a critical exponent case

Linked the equation to scalar curvature and conformal deformation problems

Abstract

Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent. On one hand, such an equation generalizes the traditional Schrodinger-Newton and Choquard equations, while, on the other hand, it is naturally related to problems involving scalar curvature and conformal deformation of metrics.