A counterexample in a unique continuation problem (Q1903139)

This paper proves the following result: (i) If \(d \geq 4\), then there exists a \(d\)-multivariate function, not identically zero, which vanishes to infinite order at origin and satisfies \(|\Delta u |\leq C |x |^{-1} \nabla u\) for some constant \(C\). (ii) If \(d \geq 5\), then the function \(u\) may be selected so that in addition \(|\Delta u |\leq V |\nabla u |\), \(V \in L^d\).