Asymptotic behavior of solutions to Schr\"odinger equations near an   isolated singularity of the electromagnetic potential
  Asymptotics of solutions to Schroedinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order -1. 
Veronica Felli, Alberto Ferrero, Susanna Terracini