A quantitative version of the Gidas-Ni-Nirenberg Theorem

A celebrated result by Gidas, Ni & Nirenberg asserts that classical positive solutions to semilinear equations $-\mathrm{\Delta }u=f(u)$ in a ball vanishing at the boundary must be radial and radially decreasing. In this paper we consider small perturbations of this equation and study the quantitative stability counterpart of this result.