An observability estimate for the heat equation from a product of two measurable sets

This paper presents an observability estimate for the heat equation in Ω × ( 0 , T ) , where Ω has a real analytic boundary ∂ Ω . The observation region is ω × E , where ω and E are positive measurable subsets of Ω and ( 0 , T ) respectively. The building of this estimate is based on a slightly modified version of the new estimate established in Apraiz and Escauriaza (2012) [15], the technique developed in Phung and Wang (2012) [11] and the shortcut of the Lebeau–Robbiano strategy provided in Miller (2010) [3].