Ninth MSU-UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 20 (2013), pp. 39-51.

A priori estimates for a critical Schrodinger-Newton equation

Marcelo M. Disconzi

Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent. On the 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.

Published October 31, 2013.
Math Subject Classifications: 35J60.
Key Words: Elliptic equation; critical exponent; a priori estimates; Schrodinger-Newton.

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Marcelo M. Disconzi
Department of Mathematics
Vanderbilt University
Nashville, TN 37240, USA

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