On the stability of the Serrin problem

We investigate stability issues concerning the radial symmetry of solutions to Serrinʹs overdetermined problems. In particular, we show that, if u is a solution to Δu=n in a smooth domain , u=0 on ∂Ω and Du is “close” to 1 on ∂Ω, then Ω is “close” to the union of a certain number of disjoint unitary balls.