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}.
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}
}