17 citations · 32 across the 12 of their papers we have counts for
12 papers
Nonlocal Ordered Mean Curvature with Integrable Kernel
Animesh Biswas, Mikil D Foss, Petronela Radu
In this paper we introduce and study the concept of nonlocal ordered curvature. In the classical (differential) setting, the problem was introduced by Nirenberg and Li, where they…
Nonlocal Green theorems and Helmholtz decompositions for truncated fractional gradients
José C. Bellido, Javier Cueto, Mikil Foss +1
In this work we further develop a nonlocal calculus theory (initially introduced in [5]) associated with singular fractional-type operators which exhibit kernels with finite suppor…
Nonlocal Mean Curvature with Integrable Kernel
Animesh Biswas, Mikil Foss, Petronela Radu
We study the prescribed constant mean curvature problem in the nonlocal setting where the nonlocal curvature has been defined as $$ H^J_Ω(x):=\int_{\mathbb{R} ^n} J(x-y)(χ_{Ω^c}(y)…
Sensitivity analysis for solutions to heterogeneous nonlocal systems
Nicole Buczkowski, Mikil Foss, Michael Parks +1
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators app…
Convergence Analysis and Numerical Studies for Linearly Elastic Peridynamics with Dirichlet-Type Boundary Conditions
Mikil Foss, Petronela Radu, Yue Yu
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditio…
Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications
M. D'Elia, C. Flores, X. Li +2
Nonlocal operators that have appeared in a variety of physical models satisfy identities and enjoy a range of properties similar to their classical counterparts. In this paper we o…