Unique continuation estimates for Baouendi--Grushin equations on cylinders

2024/01/31 by Paul Alphonse, Alphonse, Paul, Albrecht Seelmann +1 · 1 citation
Computer Science · Mathematics · #35P05 #35P10 #93B05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2401.17782

openalex publication_date 2024/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove time-pointwise quantitative unique continuation estimates for the evolution operators associated to (fractional powers of) the Baouendi--Grushin operators on the cylinder ℝ^d × \mathbbT^d. Corresponding spectral inequalities, relating for functions from spectral subspaces associated to finite energy intervals their L²-norm on the whole cylinder to the L²-norm on a suitable subset, and results on exact and approximate null-controllabilty are deduced. This extends and complements results obtained recently by the authors and by Jaming and Wang.

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