A H "older Infinity Laplacian obtained as limit of Orlicz Fractional\n Laplacians

2018/07/04 by Julián Fernández Bonder, Bonder, Julián Fernández, Mayte Pérez‐Llanos +3 · 4 citations
Computer Science · Mathematics · #35R09 #35R11 #45G05 #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.1807.01669

openalex publication_date 2018/07/04 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

This paper concerns the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators includes the fractional pn-Laplacian when pn→ ∞ as a particular case, tough it could be extended to a function of the Hölder quotient of order s, whose primitive is an Orlicz function satisfying appropriated growth conditions. The limit equation involves the Hölder infinity Laplacian.

Cited by

• Intrinsic Scalings with Non-standard Growth
• The Hénon equation in Orlicz-Sobolev spaces
• Superlinear fractional Φ-Laplacian type problems via the nonlinear Rayleigh quotient with two parameters
• Comparison principle for Singular Fractional g- Laplacian Problems

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• Hölder extension for fractional Laplacian
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• Asymptotics of Dirichlet Problems to Fractional p-Laplacian Functionals-Approach in De Giorgi Sense