Unique continuation for Schrödinger operators with potential in Morrey spaces
Copyright policy )Unique continuation for Schrödinger operators with potential in Morrey spaces
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.
Schrödinger operator, Schrödinger equation, General theory of partial differential operators, Schrödinger operators with potential in Morrey spaces, Carleman estimate
Schrödinger operator, Schrödinger equation, General theory of partial differential operators, Schrödinger operators with potential in Morrey spaces, Carleman estimate
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