In this paper, we study positive solutions u of the homogeneous Dirichlet problem for the p-Laplace equation \(-\Delta _p \,u=f(u)\) in a bounded domain \(\Omega \subset {\mathbb {R}}^N\) , where \(N\ge 2\) , \(1<p<+\infty \) and f is a discontinuous function. We address the quantitative stability of a Gidas–Ni–Nirenberg type symmetry result for u, which was established by Lions [24] and Serra [29] when \(\Omega \) is a ball. By exploiting a quantitative version of the Pólya–Szegö principle, we prove that the deviation of u from its Schwarz symmetrization can be estimated in terms of the isoperimetric deficit of \(\Omega \) .
