A Liouville-type property for degenerate-elliptic equations modeled on Hörmander vector fields
Stefano Biagi, Dario Daniele Monticelli, Fabio Punzo · Transactions of the American Mathematical Society · 2025
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.