English

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