By Hermann Dinges
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Extra resources for Martingales; a report on a meeting at Oberwolfach May 17-23, 1970
P might not be a single valued function. A further Fig. 62) where r = ro u q u r2 , is the decomposition of an into its connex components, r o is one of these components, (the outside boundary of n if n is bounded for example), and r l , r 2 , ... , are the other compon› ents. 62). Q). 38 The steady-state Stokes equations Ch. 5. Assume that a vector function w in WA,l(n), n open set of ~2 , is divergence free. 62) and w = (D2 p,-D l pl. 63) Proof. Let us first show this result for smooth functions w.
27) which completely defines rhu E Wh . 2. The preceding ex ternal approximation of stable and convergent. Hb (n) is Proof. The approximation is stable since the prolongation operators are stable. 6. 1. 28) 52 The steady-state Stokes equations Ch. 29) 0i’h U ~ DiU in L (0), as h rr I), Proof. 32) . Then Ct(u) x Sup IUh (x)-u(x) I ~ --Ihl . 33) E On the set O-O(h), lu(x)1 ~ Cl (u)d(x, IUh(X)-u(x)1 ~Ct I’) , (u)d(O(h), f). 35) which converges to 0 as h ~ 0; uh converges to u in L" (0) and then in L2 (0) since 0 is bounded.
Condition (e2) is satisfied. Proof. Let there be given a sequence uh’ E Wh " h’-. O. 38) in the weak topology of L 2 (0);
Martingales; a report on a meeting at Oberwolfach May 17-23, 1970 by Hermann Dinges