A symmetrization result for nonlinear elliptic equations (Q1884135)

The authors consider the following problem \[ -\Delta_pu=c|u|^{p-2}u+f\text{ in }\Omega\qquad u=0\text{ on }\partial\Omega,\tag{1} \] where \(\Delta_p\) is the \(p\)-Laplacian operator, \(p>1\), and \(c,f\) are bounded given functions. Under some natural assumptions on the data of (1), the authors prove that the rearrangement of \(u\) can be estimated by the solution of a problem whose data are radially symmetric.