Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I read this:

We see that $$\frac{1}{2}\lVert u(T) \rVert^2_{L^2} \leq \frac{1}{2}\lVert u(0) \rVert^2_{L^2} + \lVert f \rVert_{L^2(0,T;H^{-1})}\lVert u \rVert_{L^2(0,T;H^1_0)}$$ and since $T$ is arbitrary, we have $$\lVert u \rVert^2_{L^\infty(0,T;L^2)} \leq \lVert u(0) \rVert^2_{L^2} + \lVert f \rVert^2_{L^2(0,T;H^{-1})}$$

How is that true? I see he used Young's inequality on the RHS but what happened to the other term of Young's inequality?

share|cite|improve this question
Can you give a reference to the source of this statement? – user53153 Feb 2 '13 at 4:35
@5PM See, page 66. – george.s Feb 2 '13 at 9:41

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.