Electromagnetics - Modelling, Simulation, Control and Industrial Applications - Abstract

Pauly, Dirk

The Maxwell constants are bounded by the Poincare constants

We show that for bounded and convex domains in three dimensions, the Maxwell constants do not depend on the tangential or normal boundary condition and that these constants are bounded from below and above by the Poincare constants. In other words, the second Maxwell eigenvalues lie between the second Neumann-Laplace and the first Dirichlet-Laplace eigenvalue. Our results extend to any dimensions and partially also to mixed boundary conditions. At the end of the talk we also may present some new Poincare-type inequalities with applications in elasticity, plasticity, fluid dynamics and electro-magnetics. bf Key words:
Maxwell constants, explicit bounds