dc.contributor.author Biccari, U. dc.date.accessioned 2016-06-13T13:33:49Z dc.date.available 2016-06-13T13:33:49Z dc.date.issued 2014-12-31 dc.identifier.issn 0363-0129 dc.identifier.uri http://hdl.handle.net/20.500.11824/235 dc.description.abstract We analyse the interior controllability problem for a non-local Schr\"odinger equation involving the fractional Laplace operator $(-\Delta)^s$, $s\in(0,1)$, on a bounded $C^{1,1}$ domain $\Omega\subset\mathbb{R}^n$. The controllability from a neighbourhood of the boundary of the domain is obtained for exponents $s$ in the interval $[1/2,1)$, while for $s<1/2$ the equation is shown to be not controllable. As a consequence of that, we obtain the controllability for a non-local wave equation involving the higher order fractional Laplace operator $(-\Delta)^{2s}=(-\Delta)^s(-\Delta)^s$, $s\in[1/2,1)$. The results follow from a new Pohozaev-type identity for the fractional Laplacian recently proved by X. Ros-Oton and J. Serra and from an explicit computation of the spectrum of the operator in the one dimensional case. dc.format application/pdf dc.language.iso eng en_US dc.publisher dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title Internal control for non-local Schrodinger and wave equations involving the fractional Laplace operator dc.type info:eu-repo/semantics/article en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US
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