TY - JOUR

T1 - Some Quantitative Unique Continuation Results for Eigenfunctions of the Magnetic Schrödinger Operator

AU - Davey, Blair

PY - 2014/5

Y1 - 2014/5

N2 - 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 {pipe}V(x){pipe} < 〈x〉-N and {pipe}W(x){pipe} < 〈x〉-P. For (Formula Presented), we show that if the solution u is non-zero, bounded, and u(0) = 1, then (Formula presented), 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 (Formula presented).

AB - 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 {pipe}V(x){pipe} < 〈x〉-N and {pipe}W(x){pipe} < 〈x〉-P. For (Formula Presented), we show that if the solution u is non-zero, bounded, and u(0) = 1, then (Formula presented), 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 (Formula presented).

KW - Carleman estimates

KW - Eigenfunction

KW - Elliptic partial differential equation

KW - Quantitative unique continuation

KW - Sharp constructions

UR - http://www.scopus.com/inward/record.url?scp=84897445429&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897445429&partnerID=8YFLogxK

U2 - 10.1080/03605302.2013.796380

DO - 10.1080/03605302.2013.796380

M3 - Article

AN - SCOPUS:84897445429

VL - 39

SP - 876

EP - 945

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 5

ER -