A Liouville-type property for degenerate-elliptic equations modeled on Hörmander vector fields
We obtain Liouville type theorems for degenerate elliptic equations with a drift term and a potential. The diffusion is governed by Hörmander 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.
Authors
- Stefano Biagi (ORCID: https://orcid.org/0000-0002-9694-2566)
- Fabio Punzo (ORCID: https://orcid.org/0000-0001-8596-894X)
- Dario D. Monticelli (ORCID: https://orcid.org/0000-0002-0566-2850)
Institutions
- Politecnico di Milano (IT)
Publication Details
- Journal
- Transactions of the American Mathematical Society
- Published
- 2025-09-29
- DOI
- https://doi.org/10.1090/tran/9535
- Citations
- 2
- Primary Topic
- Advanced Mathematical Modeling in Engineering
- Type
- article
- Field-Weighted Citation Impact
- 3.01