3 citations · 11 across the 16 of their papers we have counts for
18 papers
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…
Linearization and localization of nonconvex functionals motivated by nonlinear peridynamic models
Tadele Mengesha, James M. Scott
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal st…
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…
Fractional Korn's inequalities without boundary conditions
D. Harutyunyan, T. Mengesha, H. Mikayelyan +1
This work establishes fractional analogues of Korn's first and second inequalities for vector fields in fractional Sobolev spaces defined over a bounded domain. The validity of the…
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…