Unique continuation for Schrödinger operators with partially Gevrey coefficients

2024/01/26 by Filippas, Spyridon, Laurent, Camille, Léautaud, Matthieu · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2401.14820

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.

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