Peridynamics and Anisotropic Fractional Sobolev Spaces with Variable Exponents

2024/08/17 by Sabri Bahrouni, Bahrouni, Sabri, Julián Fernández Bonder +5
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2408.09170

openalex publication_date 2024/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, our primary objective is to develop the peridynamic fractional Sobolev space and establish novel BBM-type results associated with it. We also address the peridynamic fractional anisotropic p-Laplacian. A secondary objective is to explore anisotropic fractional Sobolev spaces with variable exponents, where we also derive new BBM-type results. Additionally, we address the eigenvalue problem in the isotropic case.

Related

• Anisotropic fractional Sobolev spaces with variable exponent and application to nonlocal problems
• On Fractional Anisotropic Musielak-Sobolev Spaces with Applications to Nonlocal Eigenvalue Problems
• A Bourgain-Brezis-Mironescu formula for anisotropic fractional Sobolev spaces and applications to anisotropic fractional differential equations
• Remarks on Eigenvalue Problems for Fractional p(⋅)-Laplacian
• On a scale of anisotropic Sobolev spaces