Unique continuation for Schrodinger operators with unbounded potentials

We consider unique continuation theorems for solution of inequalities ¦Δu(x)¦ ⩽ W(x) ¦u(x)¦ with W allowed to be unbounded. We obtain two kinds of results. One allows W ϵ Lploc( R n) with p ⩾ n − 2 for n > 5, p > 1 3 (2n − 1) for n ⩽ 5 . The other requires fW2 to be −Δ-form bounded for all f ϵ C0∞.