Geodesic
On variational representations of the constant in the inf sup condition for the Stokes problem
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 110-123

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We deduce variational representations of the constant $c_\Omega$ in the inf sup condition for the Stokes problem in a bounded Lipschitz domain in $\mathbb R^d$, $d\geq2$. For any pair of admissible functions the respective variational functional provides an upper bound of $c_\Omega$ and the exact infimum of it is equal to $c_\Omega$. Minimization of the functionals over suitable finite dimensional subspaces generates monotonically decreasing sequences of numbers converging to $c_\Omega$ and, therefore, they can be used for numerical evaluation of the constant. 
@article{ZNSL_2016_444_a5,
     author = {S. Repin},
     title = {On variational representations of the constant in the inf sup condition for the {Stokes} problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {110--123},
     publisher = {mathdoc},
     volume = {444},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a5/}
}
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S. Repin. On variational representations of the constant in the inf sup condition for the Stokes problem. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 45, Tome 444 (2016), pp. 110-123. http://geodesic.mathdoc.fr/item/ZNSL_2016_444_a5/