Observability Inequalities and Measurable Sets

Details Observability Inequalities and Measurable Sets Observability Inequalities and Measurable Sets

2012-02-22

arxiv.org/abs/1202.4876v4

Mathematics

Analysis of PDEs

38 pages, update a reference

Scientific paper

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

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