Orlicz-Sobolev versus Hölder local minimizer for nonlinear Robin problems

2021/12/09 by Anouar Bahrouni, Bahrouni, Anouar, Hlel Missaoui +4
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.2112.05044

openalex publication_date 2021/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish a regularity results for weak solutions of Robin problems driven by the well-known Orlicz g-Laplacian operator. Precisely, by using a suitable variation of the Moser iteration technique, we prove that every weak solution of our problem is bounded. Moreover, we combine this result with the Lieberman regularity theorem, to show that every C¹(Ω)-local minimizer is also a W^1,G(Ω)-local minimizer for the corresponding energy functional of Robin-Orlicz problem.

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