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

Blair Davey

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

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).

Original languageEnglish (US)
Pages (from-to)876-945
Number of pages70
JournalCommunications in Partial Differential Equations
Volume39
Issue number5
DOIs
StatePublished - May 2014

Keywords

  • Carleman estimates
  • Eigenfunction
  • Elliptic partial differential equation
  • Quantitative unique continuation
  • Sharp constructions

Fingerprint Dive into the research topics of 'Some Quantitative Unique Continuation Results for Eigenfunctions of the Magnetic Schrödinger Operator'. Together they form a unique fingerprint.

  • Cite this