A p(x)-version of Diaz-Saa Inequality and some applications

2017/11/12 by Jacques Giacomoni, Peter Takáč, Giacomoni, Jacques +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1711.04286

openalex publication_date 2017/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of this work is a new extension of the well known inequality by Diaz and Saa which, in our case, involves an anisotropic operator, such as the p(x)-Laplacian. Our present extension of this inequality enables us to establish several new results on the uniqueness of solutions and comparison principles for some anisotropic quasilinear elliptic equations. Our proofs take advantage of certain convexity properties of the energy functional associated with the p(x)-Laplacian.

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