A quantitative symmetry result for p-Laplace equations with discontinuous nonlinearities

In this paper, we study positive solutions u of the homogeneous Dirichlet problem for the p-Laplace equation -Δpu=f(u) in a bounded domain Ω⊂RN, where N≥2, 1<+∞ 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 Ω 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 Ω.