209 citations · 348 across the 22 of their papers we have counts for
7 papers · 1 filter
Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications
Zhaolong Han, Xiaochuan Tian
This work contributes to nonlocal vector calculus as an indispensable mathematical tool for the study of nonlocal models that arises in a variety of applications. We define the non…
Nonlocal diffusion models with consistent local and fractional limits
Qiang Du, Xiaochuan Tian, Zhi Zhou
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter , we review their formulation defined on a bounded dom…
Nonlocal Trace Spaces and Extension Results for Nonlocal Calculus
Qiang Du, Xiaochuan Tian, Cory Wright +1
For a given Lipschitz domain , it is a classical result that the trace space of is , namely any function has a well-defined $W^…
Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization
Qiang Du, Tadele Mengesha, Xiaochuan Tian
In this work, we prove some trace theorems for function spaces with a nonlocal character that contain the classical space as a subspace. The result we obtain generalizes…
A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
Marta D'Elia, Xingjie Li, Pablo Seleson +2
Local-to-Nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. T…
A physically-consistent, flexible and efficient strategy to convert local boundary conditions into nonlocal volume constraints
Marta D'Elia, Xiaochuan Tian, Yue Yu
Nonlocal models provide exceptional simulation fidelity for a broad spectrum of scientific and engineering applications. However, wider deployment of nonlocal models is hindered by…
compactness criteria with an application to variational convergence of some nonlocal energy functionals
Qiang Du, Tadele Mengesha, Xiaochuan Tian
Motivated by some variational problems from a nonlocal model of mechanics, this work presents a set of sufficient conditions that guarantee a compact inclusion in the function spac…