2020/03/20 by Villegas, Salvador
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2003.09289
Consider the equation div(φ2 ∇ σ)=0 in ℝN, where φ>0. Berestycki, Caffarelli and Nirenberg proved that if there exists C>0 such that ∫BR(φσ)2 ≤ CR2 for every R≥ 1 then σ is necessarily constant. In this paper we provide necessary and sufficient conditions on 01 and Ψ'>0, this condition is equivalent to ∫1^∞(1)/(Ψ')=∞.