Codice 29/2009 Titolo Finite Element Approximation of the Sobolev Constant Data 2009-10-21 Autore/i Antonietti, Paola F.; Pratelli, Aldo Link Download full text Abstract Denoting by $S$ the sharp constant in the Sobolev inequality in $W^{1,2}_0(B)$, being $B$ the unit ball in $R3$, and denoting by $S_h$ its approximation in a suitable finite element space, we show that $S_h$ converges to $S$ as $h->0$ with a polynomial rate of convergence. We provide both an upper and a lower bound on the rate of convergence, and present some numerical results.