Resumen de Observability Inequalities for Parabolic Equations over Measurable Sets and Some Applications Related to the Bang-Bang Property for Control Problems

J. Apraiz

• This article 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). We will provide some applications for the above-mentioned observability inequalities, the bang-bang property for the minimal time, time optimal and minimal norm control problems, and also establish new open problems related to observability inequalities and the aforementioned applications.