Unique continuation for Schr{\"o}dinger operators with partially Gevrey coefficients
Analysis of PDEs
2024-01-29 v1 Optimization and Control
Abstract
We prove a local unique continuation result for Schr\''odinger operators with time independent Lipschitz metrics and lower order terms which are Gevrey 2 in time and bounded in space. This implies global unique continuation from any open set in a connected Riemannian manifold. These results relax in the same geometric setting the analyticity assumption in time of the Tataru-Robbiano-Zuily-H\''ormander theorem for these operators. The proof is based on (i) a Tataru-Robbiano-Zuily-H\''ormander type Carleman estimate with a nonlocal weight adapted to the anisotropy of the Schr\''odinger operator and (ii) the description of the conjugation of the Schr\''odinger operator with Gevrey coefficients by this nonlocal weight.
Cite
@article{arxiv.2401.14820,
title = {Unique continuation for Schr{\"o}dinger operators with partially Gevrey coefficients},
author = {Spyridon Filippas and Camille Laurent and Matthieu Léautaud},
journal= {arXiv preprint arXiv:2401.14820},
year = {2024}
}