Superharmonicity of nonlinear ground states

The objective of our note is to prove that, at least for a convex domain, the ground state of the p-Laplacian operator ?pu = div (|Ñu|p-2 Ñu) is a superharmonic function, provided that 2 = p = 8. The ground state of ?p is the positive solution with boundary values zero of the equation div(|Ñu|p-2 Ñu) + ? |u|p-2 u = 0 in the bounded domain O in the n-dimensional Euclidean space.