0
$\begingroup$

Let the function f be: $$f(x)={\left(1-\frac{2|x|}{X}\right)}^{\alpha}, $$ $X$ is just a real parameter.

How can I find the set of $\alpha$ such that $f \in W^{1,4}([-\frac{X}{2},\frac{X}{2}])$ ? I know the definition but I'm new with this kind of question so any help is appreciated.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

Knowing the definition is enough, here: the constraining condition is that the derivative of $f$ be in $L^4$, i.e. $x^{\alpha-1}\in L^4(0,1)$ or $4(\alpha-1)>-1$

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .