Quantitative uniqueness for Schrödinger operator with regular potentials
Quantitative uniqueness for Schrödinger operator with regular potentials
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具有正势势的薛定谔算子的定量唯一性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Jean
中科院分区：
文献类型：
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作者：
Laurent Bakri;Jean
本文给出了紧致光滑流形上具有C1电磁势的薛定谔方程解的消失阶的一个精确上界。我们的主要结果是Δu + V ·u + Wu = 0的非平凡解的消失阶处处小于C（1+<$W <$C11 scin 2+<$V <$C1）.我们的方法是基于数量Carleman型不等式，它允许我们证明下面的一致加倍不等式<$u <$L2（B2 r（x 0））≤eC（1+<$W <$C11 scin 2+<$V <$C1）<$u <$L2（Br（x 0）），这意味着所需的结果。版权所有© 2013约翰威利父子有限公司.
We give a sharp upper bound on the vanishing order of solutions to the Schrödinger equation with C1 electric and magnetic potentials on a compact smooth manifold. Our main result is that the vanishing order of nontrivial solutions to Δu + V · ∇ u + Wu = 0 is everywhere less than C(1+∥W∥C11∕2+∥V∥C1) . Our method is based on quantitative Carleman type inequalities, and it allows us to show the following uniform doubling inequality ∥u∥L2(B2r(x0))≤eC(1+∥W∥C11∕2+∥V∥C1)∥u∥L2(Br(x0)), which implies the desired result. Copyright © 2013 John Wiley & Sons, Ltd.