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Register a new userCarleman Estimate for Ultrahyperbolic Operators and Improved Interior Control for Wave Equations
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Authors
Vaibhav Kumar Jena
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In this article, we present a novel Carleman estimate for ultrahyperbolic operators, in $ R^m_t times R^n_x $. 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 compared to standard Carleman estimate results, and (2) we also prove observability when the observation point lies inside the domain. Finally, as a corollary of the observability result, we obtain improved interior controllability for the wave equation.
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