Global hypoellipticity and solvability for a class of evolution operators in time-periodic weighted Sobolev spaces

Fernando de Ávila Silva; Matteo Bonino; Sandro Coriasco

Global hypoellipticity and solvability for a class of evolution operators in time-periodic weighted Sobolev spaces

Analysis of PDEs 2025-04-04 v2

Authors: Fernando de Ávila Silva , Matteo Bonino , Sandro Coriasco

Abstract

We study the hypoellipticity and solvability properties of a class of time-periodic evolution operators, with coefficients globally defined on $\mathbb{R}^d$ and growing polynomially with respect to the space variable. To this aim, we introduce a class of time-periodic weighted Sobolev spaces, whose elements are characterised in terms of suitable Fourier expansions, associated with elliptic operators.

Keywords

global hypoellipticity solvability evolution operators time-periodic weighted Sobolev spaces Fourier expansions

Cite

@article{arxiv.2501.03414,
  title  = {Global hypoellipticity and solvability for a class of evolution operators in time-periodic weighted Sobolev spaces},
  author = {Fernando de Ávila Silva and Matteo Bonino and Sandro Coriasco},
  journal= {arXiv preprint arXiv:2501.03414},
  year   = {2025}
}

Comments

37 pages. This is the second version. Title updated, new section added, misprints corrected. Some further changes might be performed in the next versions

Related papers

View all related →