Some Quantitative Unique Continuation Results for Eigenfunctions of the Magnetic Schrödinger Operator
Some Quantitative Unique Continuation Results for Eigenfunctions of the Magnetic Schrödinger Operator
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DOI：
10.1080/03605302.2013.796380
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发表时间：
2012-09
影响因子：
1.9
通讯作者：
Blair Davey
中科院分区：
文献类型：
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作者：
Blair Davey
我们证明了-qu + vu =λu的量子，其中λ∈ℂ和v和w是满足| v（x）|是非零，有限的，u（0）= 1，然后m（r）≳ Exp（-crβ0（log r）A（r），在n，p和λ的某些条件下，我们构建了示例（其中一些是Meshkov的样式），证明了M（R）的估计值为⟩ -p和| u（x）|
We prove quantitative unique continuation results for solutions of −Δu + W · ∇u + Vu = λu, where λ ∈ ℂ and V and W are complex-valued decaying potentials that satisfy |V(x)| < ⟨x⟩−N and |W(x)| < ⟨x⟩−P . For M(R) = inf|x 0| = R ‖u‖ L 2(B 1(x 0)), we show that if the solution u is non-zero, bounded, and u(0) = 1, then M(R) ≳ exp(−CR β0 (log R) A(R)), where . Under certain conditions on N, P and λ, we construct examples (some of which are in the style of Meshkov) to prove that this estimate for M(R) is sharp. That is, we construct functions u, V and W such that −Δu + W · ∇u + Vu = λu, |V(x)| < ⟨x⟩−N , |W(x)| < ⟨x⟩−P and |u(x)|