Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using an 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 homogeneity of order -1.
Felli, V., Ferrero, A., Terracini, S. (2011). Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 13(1), 119-174 [10.4171/JEMS/246].
Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
FELLI, VERONICA;FERRERO, ALBERTO;TERRACINI, SUSANNA
2011
Abstract
Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using an 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 homogeneity of order -1.
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