Title: Time optimal boundary controls for the heat equation

The fact that the time optimal controls for parabolic equations have the bang-bang property has been recently proved 
for distributed controls. The aim of this talk consists in showing that the same property holds for boundary controls of the 
heat equation in rectangular domains. This objective is achieved by combining results and methods from traditionally distinct fields: 
the Lebeau-Robbiano strategy and estimates of the controllability cost in small time for parabolic systems, on one side, and Remez-type
 inequality for M¸ntz spaces and an inequality of Turn, on the other side.