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Unique continuation for Schrödinger operators with potential in Morrey spaces. (English) Zbl 0809.47046

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.

MSC:

47F05 General theory of partial differential operators
35J10 Schrödinger operator, Schrödinger equation
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