Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions
Analysis of PDEs
2023-08-11 v1
Abstract
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 operator that recovers the classical boundary integral, which, along with the variational analysis established previously, leads to the well-posedness of these nonlocal problems with various types of classical local boundary conditions. We continue our analysis via boundary-localized convolutions, using them to analyze the Euler-Lagrange equations, which permits us to establish global regularity properties and classical Sobolev convergence to their classical local counterparts.
Keywords
Cite
@article{arxiv.2308.05180,
title = {Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions},
author = {James M. Scott and Qiang Du},
journal= {arXiv preprint arXiv:2308.05180},
year = {2023}
}