| Abstract: |
| We establish several a priori estimates of local or global nature in Sobolev spaces with general exponent $s \leq 0$ for a class of second-order hyperbolic operators with double characteristics in presence of a transition in a domain of the Euclidian space $\mathbb{R}^3$. Then, we study the Cauchy-Dirichlet problem for a class of hyperbolic second order operators with double characteristics in presence of transition in a domain of $\mathbb{R}^3$. In particular, we obtain some existence results. |
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