ABSTRACT
This last lemma has an interesting geometric interpretation. From the (7 .2-9)
we conclude that the vector dW(w0 )jdw is colinear with the outer normal vector to j(aE n W) at f(z0 ). That is, the level hypersurfaces of 'I' and
Several interesting special cases of Lemma 7 .2f can be obtained by placing
restrictions on the domain E c en. For our next result we select E to be a Reinhart domain B2p(r). This domain is defined by
and
Proof. We prove this result by applying Lemma 7 .2.e with the special
functions n q>(w) = 'lf(w) = L I Wj I2P,
j=l
hood Vof f(JB2P) such that 'I' E C 2 (V, JR) . Note also in this case that the
norm II· 11 2p is strictly convex. Applying a version of the maximum modulus
z E JB2p(r). With these preliminaries, relations (7 .2-14) and (7.2-15) follow
from (7.2-4) and (7.2-5) of Lemma 7.2.f.
