We obtain a representation formula for solutions to Schrödinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the sharp L1→L∞ time decay estimate for the 3D-inverse square and the 2D-Aharonov–Bohm potentials.
Fanelli, L., Felli, V., Fontelos, M., Primo, A. (2013). Time Decay of Scaling Critical Electromagnetic Schrödinger Flows. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 324(3), 1033-1067 [10.1007/s00220-013-1830-y].
Time Decay of Scaling Critical Electromagnetic Schrödinger Flows
FELLI, VERONICA;
2013
Abstract
We obtain a representation formula for solutions to Schrödinger equations with a class of homogeneous, scaling-critical electromagnetic potentials. As a consequence, we prove the sharp L1→L∞ time decay estimate for the 3D-inverse square and the 2D-Aharonov–Bohm potentials.
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