Geodesic
On constants in Maxwell inequalities for bounded and convex domains
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 46-54

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For a bounded and convex domain $\Omega\subset\mathbb R^3$ we show that the Maxwell constants are bounded from below and above by Friedrichs' and Poincaré's constants of $\Omega$. 
@article{ZNSL_2014_425_a3,
     author = {D. Pauly},
     title = {On constants in {Maxwell} inequalities for bounded and convex domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {46--54},
     publisher = {mathdoc},
     volume = {425},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a3/}
}
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D. Pauly. On constants in Maxwell inequalities for bounded and convex domains. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 46-54. http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a3/