Let L be a sub-Laplacian on LN and let G = (LN, ◦, δλ) be its related homogeneous Lie group. Let E be a Euclidean subgroup of LN such that the orthonormal projection π: G -→ E is a homomorphism of homogeneous groups, and let (,) be an inner product in E. Given α ∈ E, α = 0, define Ω(α): = {x ∈ G: (α, π(x)) > 0}. We prove the following Liouville-type theorem. If u is a nonnegative L-superharmonic function in Ω(α) such that u ∈ L1(Ω(α)), then u ≡ 0 in Ω(α)

A LIOUVILLE-TYPE THEOREM ON HALF-SPACES FOR SUB-LAPLACIANS

KOGOJ, ALESSIA ELISABETTA
2015

Abstract

Let L be a sub-Laplacian on LN and let G = (LN, ◦, δλ) be its related homogeneous Lie group. Let E be a Euclidean subgroup of LN such that the orthonormal projection π: G -→ E is a homomorphism of homogeneous groups, and let (,) be an inner product in E. Given α ∈ E, α = 0, define Ω(α): = {x ∈ G: (α, π(x)) > 0}. We prove the following Liouville-type theorem. If u is a nonnegative L-superharmonic function in Ω(α) such that u ∈ L1(Ω(α)), then u ≡ 0 in Ω(α)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2642986
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