Maximum principles and moving planes method for the fractional p(x,⋅)-Laplacian

2024/04/02 by Anouar Bahrouni, Bahrouni, Anouar, Abdelhakim Sahbani +3
Computer Science · Mathematics · #35G30 #35J20 #35J35 #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2404.01759

openalex publication_date 2024/04/02 · openalex created_date 2024/04/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the monotonicity of solutions for a nonlinear equations involving the fractional Laplacian with variable exponent. We first prove different maximum principles involving this operator. Then we employ the direct moving planes method to obtain monotonicity of solutions to a nonlinear equations in which the fractional laplacian with variable exponent is present. Note that, there are no results studying the monotonicity of solutions for local or nonlocal equations with variables exponent. Our results are new in this setting and includes a self-contained techniques.

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