A Liouville theorem for -harmonic functions on exterior domains

摘要

We prove Liouville type theorems for -harmonic functions on exterior domains of , where and . We show that every positive -harmonic function satisfying zero Dirichlet, Neumann or Robin boundary conditions and having zero limit as tends to infinity is identically zero. In the case of zero Neumann boundary conditions, we establish that any semi-bounded -harmonic function is constant if . If , then it is either constant or it behaves asymptotically like the fundamental solution of the homogeneous -Laplace equation.