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(i) Let, and let be densely in and continuously imbedded into it,. .
Let, and let be densely in and continuously imbedded into it,.
Let X be a Banach space continuously imbedded into a Banach space Y, and let D be a group of linear isometric operators on X.
Thus the assertion of the lemma follows from Lemma 4.2 with noting that the space V 2, m + ε 2 m is continuously imbedded in H m + ε 2 m according to (2.1).
(Vhookrightarrow H) is continuous and V is dense in H. Then ({uin L^{2} 0, T; V)|u_{t}in L^{2} 0, T; V')}) is continuously imbedded in (C [0, T]; H)).
Here we remark that W is continuously imbedded in C ( [ 0, T ] ; V ) ∩ C 1 ( [ 0, T ] ; V ), so that we assume that there exists | ∇ y ( t ) | < C, | d d t ∇ y ( t ) | < C. (2.1).
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