Abstract
AbstractWe discuss the well-posedness of the Cauchy problem for noneffectively hyperbolic operators assuming that the spectral structure of the Hamilton map changes across a submanifold of codimension 1 of the double characteristic manifold. Under the assumption that there is no null bicharacteristic tangent to the submanifold where the spectral transition occurs, we derive microlocal a priori estimates assuming the strict Ivrii-Petkov-Hörmander condition.Key wordsCauchy problemHamilton map and flowTransition caseNoneffectively hyperbolic operator
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