PreprintCC BY 4.0arXiv
Carleman Estimates for Critical Electromagnetic Schrödinger Operators on Conic Manifolds
Abstract
We establish an Lp--Lq-type Carleman estimate for the Schrödinger operator HA,V with scaling-critical electromagnetic singular potentials on a conical singular space (X,g) of dimension d≥3, where the metric is g=dr2+r2h and X=C(Y)=(0,∞)r× Y is a product cone over the closed Riemannian manifold (Y,h). More precisely, we prove |eτϕu|L2d/(d−2)(X)≤ C |eτϕHA,Vu|L2d/(d+2)(X) with the quadratic weight ϕ(r)=1/4(log r)2, uniformly in τ. As an application of this Carleman estimate, we prove the unique continuation property for this electromagnetic Schrödinger operator when the cross-section is Y=𝕊d−1.
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BibTeX
@misc{yin2026carleman,
title = {{Carleman Estimates for Critical Electromagnetic Schrödinger Operators on Conic Manifolds}},
author = {Baiyang Yin and Fang Zhang and Junyong Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09721},
eprint = {2610.09721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09721},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Carleman Estimates for Critical Electromagnetic Schrödinger Operators on Conic Manifolds
AU - Baiyang Yin
AU - Fang Zhang
AU - Junyong Zhang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09721
UR - https://arxiv.org/abs/2610.09721
AB - We establish an L^p--L^q-type Carleman estimate for the Schrödinger operator H_A,V with scaling-critical electromagnetic singular potentials on a conical singular space (X,g) of dimension d≥3, where the metric is g=dr^2+r^2h and X=C(Y)=(0,∞)_r× Y is a product cone over the closed Riemannian manifold (Y,h). More precisely, we prove |e^τϕu|_L^2d/(d−2)(X)≤ C |e^τϕH_A,Vu|_L^2d/(d+2)(X) with the quadratic weight ϕ(r)=1/4(log r)^2, uniformly in τ. As an application of this Carleman estimate, we prove the unique continuation property for this electromagnetic Schrödinger operator when the cross-section is Y=𝕊^d−1.
ER -