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.

$$ f \in C^0 ([0,1] , W^{3,2} (K) ) $$

Here $W^{n,m}$ is a Sobolev Space, and K is a subset of $\mathbb R^3$ .

share|improve this question
    
@DavideGiraudo $f$ is a function defined on $[0, \infty) \times \mathbb R^3$. –  Misaj May 27 '12 at 10:15

1 Answer 1

up vote 0 down vote accepted

$f$ is a continuous map from the unit interval into the function space $W^{3,2}(K)$.

Edit (after OP made his question more precise):

If $f:[0,\infty)\times \mathbb{R}^3 \rightarrow \mathbb{R}$

then $t\mapsto f(t, .)$ may be viewed as a map from the positive real axis to maps $\mathbb{R}^3 \rightarrow \mathbb{R}$

By restriction (on both arguments), such a map gives rise to a map $[0,1]\rightarrow \{\phi: K\rightarrow \mathbb{R}\}$. Then your notation means that for this restriction the first sentence of my answer applies.

share|improve this answer
    
oh I'm sorry. $f$ was a function defined on $[0,∞) \times \mathbb R^3 $. –  Misaj May 27 '12 at 10:17
    
Then the notation says that the corresponding restriction of the first argument of $f$ to $[0,1]$, when viewed as a map from $K$ to $\mathbb{R}$, has the property I wrote down. –  user20266 May 27 '12 at 10:19

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.