Observability Inequalities and Measurable Sets

Abstract

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.

To appear in JEMS

Cited by in corpus (2)

• Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map
• Observations from measurable sets and applications