We prove weighted L^p-Liouville theorems for a class of second-order hypoelliptic partial differential operators L on Lie groups G whose underlying manifold is n-dimensional space. We show that a natural weight is the right-invariant measure ˇH of G. We also prove Liouville-type theorems for C^2 subsolutions in L p(G, ˇH ). We provide examples of operators to which our results apply, jointly with an application to the uniqueness for the Cauchy problem for the evolution operator L − ∂t .
Andrea Bonfiglioli, Alessia Elisabetta Kogoj (2016). Weighted L^p-Liouville theorems for hypoelliptic partial differential operators on Lie groups. JOURNAL OF EVOLUTION EQUATIONS, 16, 569-585 [10.1007/s00028-015-0313-3].
Weighted L^p-Liouville theorems for hypoelliptic partial differential operators on Lie groups
BONFIGLIOLI, ANDREA;KOGOJ, ALESSIA ELISABETTA
2016
Abstract
We prove weighted L^p-Liouville theorems for a class of second-order hypoelliptic partial differential operators L on Lie groups G whose underlying manifold is n-dimensional space. We show that a natural weight is the right-invariant measure ˇH of G. We also prove Liouville-type theorems for C^2 subsolutions in L p(G, ˇH ). We provide examples of operators to which our results apply, jointly with an application to the uniqueness for the Cauchy problem for the evolution operator L − ∂t .I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
