ABSTRACT
Then, estimate (2.1.10) holds true for r > 0 sufficiently large, with the boundary terms (BT)\z replaced by (£?T)|Sl i.e., evaluated only on Ei = [0, T] x IV G
The proof of Theorem 2.1.2 will be given in Section 2.3. As a consequence of Theorem 2.1.2 and of a uniqueness theorem, we then obtain the desired "continuous observability inequality" for the homogeneous problem
< </>(0, • ) = </>0; </>t(0, • ) = Vi in H; (2.1.15b)
( VIL = 0 in (0, T] x T = E, (2.1.15c) where F is the first-order linear operator in (2.1.2). The reverse "trace regularity inequality" was proved in [L-L-T.l, [Li.l], [L-T,l] for any T > 0.
