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Quantitative uniqueness for Schrödinger operator with regular potentials |
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| Authors: | Laurent Bakri Jean‐Baptiste Casteras |
| Institution: | 1. Group of Analysis & Mathematic modeling, Departamento de Matemática, Universidad Técnica Federico Santa Maria, , Avenida Espa?a, Valparíso, Chile. This author was partially supported by programa Basal CMM, Universidad de Chile;2. Laboratoire de Mathématiques (UMR CNRS 6205), Université de Bretagne Occidentale, , 29238 Brest Cedex 3, France |
| Abstract: | We give a sharp upper bound on the vanishing order of solutions to the Schrödinger equation with  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  . Our method is based on quantitative Carleman type inequalities, and it allows us to show the following uniform doubling inequality |
| Keywords: | quantitative unique continuation Carleman inequalities three balls inequalities doubling estimates Schrö dinger operator linear elliptic problem |