On parameterized nonlocal-fractional transmission problems and associated function spaces
Analysis of PDEs
2025-09-30 v1
Abstract
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a fractional type Dirichlet energy on one subdomain and a nonlocal Dirichlet energy involving a finite range of interactions on another subdomain. We present the rigorous mathematical formulation and its well-posedness. We also investigate the behavior of the model in various limiting regimes.
Cite
@article{arxiv.2509.22987,
title = {On parameterized nonlocal-fractional transmission problems and associated function spaces},
author = {Qiang Du and Zhaolong Han and Tadele Mengesha and James M. Scott and Xiaochuan Tian},
journal= {arXiv preprint arXiv:2509.22987},
year = {2025}
}