Resumen de A simple proof of the optimal power in Liouville theorems
Consider the equation div(ϕ2∇σ) = 0 in RN , where ϕ > 0. It is well known [4, 2] that if there exists C > 0 such that R BR (ϕσ) 2 dx ≤ CR2 for every R ≥ 1, then σ is necessarily constant. In this paper we present a simple proof that this result is not true if we replace R2 with Rk for k > 2 in any dimension N. This question is related to a conjecture by De Giorgi.
