APDE seminar@BCAM: Quantitative propagation of smallness in the plane and 1D spectral estimates

We investigate the connection between the propagation of smallness in two dimensions and one-dimensional spectral estimates. The propagation of smallness in the plane obtained by Y. Zhu, reveals how the value of solutions in a small region extends to a larger domain. By revisiting Zhu’s proof, we obtain a quantitative version that includes an explicit dependence on key parameters. This refinement enables us to establish spectral inequalities for one-dimensional Schrödinger operators.