1 citations · 1 across the 3 of their papers we have counts for
3 papers
math.AP2023
Existence and uniqueness of solutions to the Peierls-Nabarro model in anisotropic media
Yuan Gao, James M. Scott
We study the existence and uniqueness of solutions to the vector field Peierls-Nabarro model for curved dislocations in a transversely isotropic medium. Under suitable assumptions…
math.AP2023★ 1 cited
Nonlocal boundary-value problems with local boundary conditions
James M. Scott, Qiang Du
We describe and analyze nonlocal integro-differential equations with classical local boundary conditions. The interaction kernel of the nonlocal operator has horizon parameter depe…
math.AP2021
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
Marta D'Elia, Mamikon Gulian, Tadele Mengesha +1
Nonlocal vector calculus, which is based on the nonlocal forms of gradient, divergence, and Laplace operators in multiple dimensions, has shown promising applications in fields suc…