Some a priori estimates for a critical Schrodinger-Newton equation

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.