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Resolvent estimates and matrix-valued Schrodinger operator with eigenvalue crossings; Application to Strichartz estimates

Abstract : We consider a semi-classical Schrodinger operator with a matrix-valued potential presenting eigenvalue crossings on isolated points. We obtain estimates for the boundary values of the resolvent under a generalized non-trapping assumption. As a consequence, we prove the smoothing effect of this operator, derive Strichartz type estimate for the propagator and get an existence theorem for a system of non-linear Schrodinger equations.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693084
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Submitted on : Tuesday, May 1, 2012 - 8:03:12 PM
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Clotilde Fermanian Kammerer, Vidian Rousse. Resolvent estimates and matrix-valued Schrodinger operator with eigenvalue crossings; Application to Strichartz estimates. Communications in Partial Differential Equations, Taylor & Francis, 2008, 33 (1), pp.19--44. ⟨10.1080/03605300701454925⟩. ⟨hal-00693084⟩

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