Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions

James M. Scott; Qiang Du

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arXiv · 2308.05180

Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions

James M. Scott·Qiang Du

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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.

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James M. Scott, Qiang Du. 2023-08-09. Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions. https://arxiv.org/abs/2308.05180

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