Null controllability of the heat equation with boundary Fourier conditions: the linear case

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form . We consider distributed controls with support in a small set and nonregular coefficients . For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.