Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces
Analysis of PDEs
2025-06-17 v1
Abstract
We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of singular solutions, we fully characterize when the system fails to be globally hypoelliptic.
Keywords
Cite
@article{arxiv.2506.12178,
title = {Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces},
author = {Fernando de Ávila Silva and Marco Cappiello and Alexandre Kirilov},
journal= {arXiv preprint arXiv:2506.12178},
year = {2025}
}