Peridynamics and Anisotropic Fractional Sobolev Spaces with Variable Exponents

TL;DR

This paper develops new mathematical frameworks for peridynamic fractional Sobolev spaces, including anisotropic and variable exponent cases, establishing BBM-type results and analyzing eigenvalue problems.

Contribution

It introduces novel peridynamic fractional Sobolev spaces with anisotropic and variable exponents, and derives new BBM-type results and eigenvalue analysis.

Findings

Established BBM-type results for new Sobolev spaces

Analyzed eigenvalue problems in isotropic cases

Extended Sobolev space theory to anisotropic and variable exponent contexts

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.