English

On some properties of weak solutions to the Maxwell equations

Analysis of PDEs 2021-05-18 v1

Abstract

This paper is concerned with weak solutions {e,h} in L^2 x L^2 of the time-dependent Maxwell equations. We show that these solutions obey an energy equality. Our method of proof is based on the approximation of {e,h} by its Steklov mean with respect to time t. This approximation technique is well-known for establishing integral estimates for weak solutions of parabolic equations. In addition we prove the uniqueness of {e,h}.

Keywords

Cite

@article{arxiv.2105.07063,
  title  = {On some properties of weak solutions to the Maxwell equations},
  author = {Joachim Naumann},
  journal= {arXiv preprint arXiv:2105.07063},
  year   = {2021}
}