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Observability inequalities and measurable sets

Jone ApraizLuis EscauriazaGengsheng WangC. Zhang — 2014

Journal of the European Mathematical Society

This paper presents two observability inequalities for the heat equation over Ω × ( 0 , T ) . In the first one, the observation is from a subset of positive measure in Ω × ( 0 , T ) , while in the second, the observation is from a subset of positive surface measure on Ω × ( 0 , T ) . It also proves the Lebeau-Robbiano spectral inequality when Ω is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.

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