Abstract
In this article, we present a novel Carleman estimate for ultrahyperbolic operators, in Rtm×Rxn. Then, we use a special case of this estimate to obtain improved observability results for wave equations with time-dependent lower order terms. The key improvements are: (1) we obtain smaller observation regions when compared with standard Carleman estimate results, and (2) we also address the case when observability is centered around a point inside the domain. Finally, as a corollary of the observability result, we obtain improved interior controllability for wave equations with same features.
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