In this paper we obtain comparison results for the quasilinear equation with homogeneous Dirichlet boundary conditions by Steiner rearrangement in variable x, thus solving a long open problem. In fact, we study a broader class of anisotropic problems. Our approach is based on a finite-differences discretization in y, and the proof of a comparison principle for the discrete version of the auxiliary problem , where . We show that this operator is T-accretive in . We extend our results for to general operators of the form where a is non-decreasing and behaves like at infinity.
Cite this article
F. Brock, J.I. Díaz, A. Ferone, D. Gómez-Castro, A. Mercaldo, Steiner symmetrization for anisotropic quasilinear equations via partial discretization. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 2, pp. 347–368DOI 10.1016/J.ANIHPC.2020.07.005