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

作者：Kogoj Alessia E^*

来源：Proceedings of the American Mathematical Society, 2015, 143(1): 239-248.

• Liouville-type theorems
• half-spaces
• superharmonic functions
• sub-Laplacians
• homogeneous Lie groups

Let L be a sub-Laplacian on L-N and let G = (L-N, o, delta(lambda)) be its related homogeneous Lie group. Let E be a Euclidean subgroup of L-N such that the orthonormal projection pi : G -> E is a homomorphism of homogeneous groups, and let < , > be an inner product in E. Given alpha is an element of E, alpha not equal 0, define Omega(alpha) := {x is an element of G : > 0}. We prove the following Liouville-type theorem.
If u is a nonnegative L-superharmonic function in O(a) such that u. L-1(Omega(alpha)), then u = 0 in Omega(alpha).

• 出版日期2015-1