Steiner symmetrization for anisotropic quasilinear equations via partial discretization

  • F. Brock

    Institute of Mathematics, University of Rostock, Germany
  • J.I. Díaz

    Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Spain; Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Spain
  • A. Ferone

    Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, Italy
  • D. Gómez-Castro

    Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Spain; Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Spain
  • A. Mercaldo

    Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Italy
Steiner symmetrization for anisotropic quasilinear equations via partial discretization cover
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Abstract

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. 347–368

DOI 10.1016/J.ANIHPC.2020.07.005