| Abstract: |
| We study the spatial decay and quantitative uniqueness properties for the
elliptic equations $\Delta u = W \cdot \nabla u$ and $\Delta u = V u$, inspired by Meshkov`s constructions addressing the Landis conjecture. We also consider the question of quantitative uniqueness for the equation $\Delta u = V u$ with either periodic or Dirichlet boundary conditions in a disk. We then show the sharpness of recently obtained bounds in the case of a parabolic equation $\partial_t u - \Delta u = V u$. |
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