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)File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
