This paper presents a new observability estimate for parabolic equations in , where is a convex domain. The observation region is restricted over a product set of an open nonempty subset of and a subset of positive measure in . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.
Cite this article
Kim Dang Phung, Gengsheng Wang, An observability estimate for parabolic equations from a measurable set in time and its applications. J. Eur. Math. Soc. 15 (2013), no. 2, pp. 681–703DOI 10.4171/JEMS/371