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].