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Article Dans Une Revue Communications in Partial Differential Equations Année : 2008

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

Résumé

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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Dates et versions

hal-00693084 , version 1 (01-05-2012)

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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, 2008, 33 (1), pp.19--44. ⟨10.1080/03605300701454925⟩. ⟨hal-00693084⟩
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