Quantitative propagation of smallness and spectral estimates for the Schrödinger operator
arxiv(2024)
摘要
In this paper, we investigate quantitative propagation of smallness
properties for the Schrödinger operator on a bounded domain in ℝ^d.
We extend Logunov, Malinnikova's results concerning propagation of smallness
for A-harmonic functions to solutions of divergence elliptic equations
perturbed by a bounded zero order term. We also prove similar results for
gradient of solutions to some particular equations. This latter result enables
us to follow the recent strategy of Burq, Moyano for the obtaining of spectral
estimates on rough sets for the Schrödinger operator. Applications to
observability estimates and to the null-controllability of associated parabolic
equations posed on compact manifolds or the whole euclidean space are then
considered.
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