English

A Liouville-type property for degenerate-elliptic equations modeled on H\"ormander vector fields

Analysis of PDEs 2025-04-09 v1

Abstract

We obtain Liouville type theorems for degenerate elliptic equation with a drift term and a potential. The diffusion is driven by H\"ormander operators. We show that the conditions imposed on the coefficients of the operator are optimal. Indeed, when they fail we prove that infinitely many bounded solutions exist.

Keywords

Cite

@article{arxiv.2504.06068,
  title  = {A Liouville-type property for degenerate-elliptic equations modeled on H\"ormander vector fields},
  author = {Stefano Biagi and Dario Daniele Monticelli and Fabio Punzo},
  journal= {arXiv preprint arXiv:2504.06068},
  year   = {2025}
}
R2 v1 2026-06-28T22:50:55.213Z