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Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions
James M. Scott, Qiang Du
We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green's identity for the nonlocal…
Nonlocal problems with local boundary conditions I: function spaces and variational principles
James M. Scott, Qiang Du
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces a…
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…
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…
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…