A-priori pseudoconvexity energy estimates in domains with boundary and applications to exact boundary controllability for conservative P.D.E.

The problem of obtaining a-priori energy estimates for nonelliptic boundary value problems has been largely studied in the last years essentially in the context of boundary observability and controllability problems for evolution equations governed by P.D.E. However, the problems were studied on a case by case basis, only for some particular types of boundary controls, and moreover, several unnatural restrictions concerning lower order terms were used.

Our first goal is to obtain a-priori energy estimates of Carleman's type but for solutions of P.D.E. in domains with boundary. This will give next a general approach for boundary controllability problems, which is valid for all evolution P.D.E of "conservative" type, all boundary controls for which the corresponding homogeneous problem is well-posed, and all well-posedness spaces for the homogeneous problem.

We say here that an evolution P.D.E. is of "conservative" type if when it is considered in R X R^no it essentially generates time reversible dynamics. Many of the math-physics equations satisfy this condition. The first example of such equations is the class of hyperbolic equations, but valid examples are also equations such as Schroedinger equation and various models for the plate equation.

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