2000 Mathematics Subject Classification: 34E20, 35L80, 35L15. In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics.
The article studies a second-order linear differential operator of the type , i. e., a sum of squares of real, and real-analytic, vector fields . The conjectured necessary and sufficient condition for analytic hypo- ellipticity, based on the Poisson stratification of the characteristic variety, is recalled in simple analytic and geometric terms. It is conjectured that the microlocal Gevrey hypo-ellipticity of depends on the restrictions of the principal symbol to or symplectic...
We study a class of third order hyperbolic operators in with triple characteristics on . We consider the case when the fundamental matrix of the principal symbol for has a couple of non vanishing real eigenvalues and is strictly hyperbolic for We prove that is strongly hyperbolic, that is the Cauchy problem for is well posed in for any lower order terms .
In questa Nota si considerano, in opportuni spazi con peso, problemi al contorno in un semispazio per operatori del tipo dove è un operatore ellittico e è un parametro complesso.
In questa nota diamo alcuni risultati su di una classe di problemi al contorno per equazioni ellittiche a coefficienti polinomiali in un semispazio. Si stabilisce 1'esistenza di una parametrice destra e di una parametrice sinistra del problema; si stabiliscono inoltre stime a priori del problema e di quello aggiunto.
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