A strong maximum principle and a compact support principle for singular elliptic inequalities

AbstractVazquez in 1984 established a strong maximum principle for the classical m-Laplace differential inequalityΔmu−f(u)≤0,where Δmu=div(|Du|m−2Du) and f(u) is a non-decreasing continuous function with f(0)=0. We extend this principle to a wide class of singular inequalities involving quasilinear divergence structure elliptic operators, and also consider the converse problem of compact support solutions in exterior domains