Unique continuation for Schrödinger operators with potential in Morrey spaces (Q1174951)

The authors prove that any solution of \[ |\Delta u(x)|\leq V(x)| u(x)|, \qquad x\in \Omega\subset R^ n, \] has the global unique continuation property if \(v\in F_{\text{loc}}^ p\) and \(p> (n- 2)/2\). \(F^ p\)-spaces introduced by Morrey have norm \[ \| v\|_{F^ p}= \sup_ Q | Q|^{2/n} \Biggl( {1\over {| Q|}} \int_ Q | v|^ p \Biggr)^{1/p}, \] where \(Q\) is a cube in \(R^ n\). This result is obtained as a consequence of certain Carleman estimate.