Comparison principles, uniqueness and symmetry results of solutions of quasilinear elliptic equations and inequalities

We prove comparison principles, uniqueness, regularity and symmetry results for p-regular distributional solutions of quasilinear very weak elliptic equations of coercive type and to related inequalities. The simplest model examples are −Δpu+|u|q−1u=hon RN, where q>p−1>0 and −div(∇u1+|∇u|2)+|u|q−1u=hon RN, with q>0 and h∈Lloc1(RN).