Comparison results for solutions to the anisotropic Laplacian with Robin boundary conditions. (January 2022)

• Record Type: Journal Article
• Authors: Sannipoli, Rossano
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 35B51 -- 35G20 -- 35G30 -- 35J60 -- 35P15; Anisotropic Laplacian -- Robin boundary conditions -- Talenti comparison result -- Bossel–Daners inequality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112615
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider PDE's problems involving the anisotropic Laplacian operator, with Robin boundary conditions. By means of Talenti techniques, widely used in the last decades, we prove a comparison result between the solutions of the above-mentioned problems and the solutions of the symmetrized ones. As a consequence of these results, a Bossel–Daners type inequality can be shown in dimension 2.