On a critical Maxwell equation in nonlocal media
Analysis of PDEs
2022-11-28 v1 Functional Analysis
Abstract
In this paper, we study the existence of solutions for a critical time-harmonic Maxwell equation in nonlocal media. By introducing some suitable Coulomb spaces involving curl operator, we are able to obtain the ground state solutions of the curl-curl equation via the method of constraining Nehari-Pankov manifold. Correspondingly, some sharp constants of the Sobolev-like inequalities with curl operator are obtained by a nonlocal version of the concentration-compactness principle.
Keywords
Cite
@article{arxiv.2211.13556,
title = {On a critical Maxwell equation in nonlocal media},
author = {Minbo Yang and Weiwei Ye and Shuijin Zhang},
journal= {arXiv preprint arXiv:2211.13556},
year = {2022}
}
Comments
33 pages. arXiv admin note: text overlap with arXiv:2002.00613 by other authors