On the Maxwell and Friedrichs/Poincaré constants in ND

  • Dirk PaulyEmail author


We prove that for bounded and convex domains in arbitrary dimensions, the Maxwell constants are bounded from below and above by Friedrichs’ and Poincaré’s constants, respectively. Especially, the second positive Maxwell eigenvalues in ND are bounded from below by the square root of the second Neumann-Laplace eigenvalue.


Maxwell’s equations Maxwell constant Second Maxwell eigenvalue Electro statics Magneto statics Poincaré inequality Friedrichs inequality Poincaré constant Friedrichs constant 

Mathematics Subject Classification

35A23 35Q61 35E10 35F15 35R45 46E40 53A45 



We cordially thank the anonymous referee for a very careful reading and valuable suggestions for improving the paper.


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Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität Duisburg-EssenEssenGermany

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