Dependence of Friedrichs' constant on boundary integrals
Giles Auchmuty, Behrouz Emamizadeh, Mohsen Zivari-Rezapour · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2005
This note extends the results in ‘Optimal coercivity inequalities in W 1, p (Ω)’ (G. Auchmuty, Proc. R. Soc. Edinb. A 135 , 915–933.) describing the dependence of the optimal constant in the p -version of Friedrichs' inequality on the boundary integral term. In particular, it is shown that this constant is continuous, increasing, concave and increases to the optimal constant for the Dirichlet problem as s → ∞.