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 .

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 .
Andrea Bonfiglioli; Alessia Elisabetta Kogoj
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/586993
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