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Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein). (English) Zbl 0593.35119
The authors prove a strong unique continuation property: Let $\Omega$ be a connected domain of ${\bbfR}\sp n$, $x\in \Omega$, $V\in L\sp{n/2}\sb{loc}({\bbfR}\sp n)$, $q=2n/(n+2)$, $u\in H\sp{2,q}\sb{loc}(\Omega)$, and $u=0$ on some nonempty subset of $\Omega$, then $u=0$ on $\Omega$. The method used is to prove a Carleman type inequality by complex interpolation. - The paper has an appendix by E. Stein where the proof is simplified and the result is extended to Lorentz spaces.
Reviewer: H.Siedentop

35R45Partial differential inequalities
35J10Schrödinger operator
35P15Estimation of eigenvalues and upper and lower bounds for PD operators
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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