English

On Maxwell's and Poincare's Constants

Analysis of PDEs 2014-03-12 v4 Numerical Analysis

Abstract

We prove that for bounded and convex domains in three dimensions, the Maxwell constants are bounded from below and above by Friedrichs' and Poincar\'e's constants. In other words, the second Maxwell eigenvalues lie between the square roots of the second Neumann-Laplace and the first Dirichlet-Laplace eigenvalue.

Keywords

Cite

@article{arxiv.1311.2186,
  title  = {On Maxwell's and Poincare's Constants},
  author = {Dirk Pauly},
  journal= {arXiv preprint arXiv:1311.2186},
  year   = {2014}
}

Comments

Key Words: Maxwell's equations, Maxwell constant, second Maxwell eigenvalue, electro statics, magneto statics, Poincare's inequality, Friedrichs' inequality, Poincare's constant, Friedrichs' constant