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.

References in corpus (5)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Gravitationally induced inhibitions of dispersion according to a modified Schrödinger-Newton equation for a homogeneous-sphere potential
• A possible experimental test of quantized gravity
• Recent progress on the Yamabe problem
• An existence theorem for the Yamabe problem on manifolds with boundary