TY - JOUR
T1 - Uniform resolvent estimates for Schrödinger operators in Aharonov-Bohm magnetic fields
AU - Gao, Xiaofen
AU - Wang, Jialu
AU - Zhang, Junyong
AU - Zheng, Jiqiang
N1 - Publisher Copyright:
© 2021
PY - 2021/8/15
Y1 - 2021/8/15
N2 - We study the uniform weighted resolvent estimates of Schrödinger operator with scaling-critical electromagnetic potentials which, in particular, include the Aharonov-Bohm magnetic potential and inverse-square potential. The potentials are critical due to the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In contrast to the Laplacian −Δ on R2, we prove some new uniform weighted resolvent estimates for this 2D Schrödinger operator and, as applications, we show local smoothing estimates for the Schrödinger equation in this setting.
AB - We study the uniform weighted resolvent estimates of Schrödinger operator with scaling-critical electromagnetic potentials which, in particular, include the Aharonov-Bohm magnetic potential and inverse-square potential. The potentials are critical due to the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In contrast to the Laplacian −Δ on R2, we prove some new uniform weighted resolvent estimates for this 2D Schrödinger operator and, as applications, we show local smoothing estimates for the Schrödinger equation in this setting.
KW - Aharonov-Bohm magnetic field
KW - Local smoothing estimates
KW - Resolvent estimates
KW - Scaling-critical electromagnetic potential
UR - http://www.scopus.com/inward/record.url?scp=85105573154&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2021.05.009
DO - 10.1016/j.jde.2021.05.009
M3 - Article
AN - SCOPUS:85105573154
SN - 0022-0396
VL - 292
SP - 70
EP - 89
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -