We obtain Liouville type theorems for degenerate elliptic equations with a drift term and a potential. The diffusion is governed 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.
A Liouville-type property for degenerate-elliptic equations modeled on Hörmander vector fields
Biagi, Stefano;Monticelli, Dario;Punzo, Fabio
2026-01-01
Abstract
We obtain Liouville type theorems for degenerate elliptic equations with a drift term and a potential. The diffusion is governed 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.File in questo prodotto:
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