Strong Unique Continuation Results for Differential Inequalities

The main result of this paper is a strong uniqueness theorem for differential inequalities of the form |Δu(x)|⩽|V(x) u(x)|+|W(x) ∇u(x)|, whereVandWare radial functions inLn/2loc(Ω) andLnloc(Ω) respectively, andΩis a connected open subset of Rn. Other results involving other spaces of potentialsVandWare proved. Our method relies on sharp Carleman estimates.