Take the 2-minute tour ×
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.

Let $f = f(t,x) = f(t, x_1, \cdots , x_n) . $ If $f \in C^1 ([0,M],W^{s,2}(\Bbb R^n))$ (which means that $g(t) :=\| f \|_{W^{s,2}(\Bbb R^n)}$ is differentiable on $[0,M]$ and $\frac{d}{dt} g(t)$ is continuous on $[0,M]$), then can I conclude that $h(t) := \| \partial_t f \|_{W^{s,2}(\Bbb R^n)} $ is also continuous on $[0,M]$?
Here $W^{s,2}$ means the general Sobolev space, and let $s$ be an integer.

share|improve this question
add comment

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.