A general framework for nonlocal Neumann problems
Analysis of PDEs
2023-12-11 v2 Probability
Abstract
Within the framework of Hilbert spaces, we solve nonlocal problems in bounded domains with prescribed conditions on the complement of the domain. Our main focus is on the inhomogeneous Neumann problem in a rather general setting. We also study the transition from complement value problems to local boundary value problems. Several results are new even for the fractional Laplace operator. The setting also covers relevant models in the framework of peridynamics.
Cite
@article{arxiv.2204.06793,
title = {A general framework for nonlocal Neumann problems},
author = {Guy Foghem and Moritz Kassmann},
journal= {arXiv preprint arXiv:2204.06793},
year = {2023}
}
Comments
Published in Commun. Math. Sci.: https://dx.doi.org/10.4310/CMS.2024.v22.n1.a2