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arXiv · 2509.22987

On parameterized nonlocal-fractional transmission problems and associated function spaces

Qiang Du·Zhaolong Han·Tadele Mengesha·James M. Scott·Xiaochuan Tian
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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.

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Qiang Du, Zhaolong Han, Tadele Mengesha, James M. Scott, Xiaochuan Tian. 2025-09-26. On parameterized nonlocal-fractional transmission problems and associated function spaces. https://arxiv.org/abs/2509.22987

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