Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications
Analysis of PDEs
2019-08-26 v1 Functional Analysis
Abstract
Nonlocal operators that have appeared in a variety of physical models satisfy identities and enjoy a range of properties similar to their classical counterparts. In this paper we obtain Helmholtz-Hodge type decompositions for two-point vector fields in three components that have zero nonlocal curls, zero nonlocal divergence, and a third component which is (nonlocally) curl-free and divergence-free. The results obtained incorporate different nonlocal boundary conditions, thus being applicable in a variety of settings.
Keywords
Cite
@article{arxiv.1908.08624,
title = {Helmholtz-Hodge decompositions in the nonlocal framework. Well-posedness analysis and applications},
author = {M. D'Elia and C. Flores and X. Li and P. Radu and Y. Yu},
journal= {arXiv preprint arXiv:1908.08624},
year = {2019}
}
Comments
17 pages, 1 figure