  In this paper, building on the ideas of Brasco and Pratelli (Geom. Funct.
Anal., 22 (2012), 107-135), we establish a stability estimate for Bucur and
Henrot's inequality (Acta Math., 222 (2019), 337-361). Their inequality asserts
that, among regular sets of given measure, the disjoint union of two balls with
the same radius maximizes the second non trivial eigenvalue of the Neumann
Laplacian.
