0
$\begingroup$

Let $n=2$ or 3 and let $\Omega$ be a bounded domain of $\mathbb{R}^n$. Let $T>0$ and $f \in L^2([0,T],H^1(\mathbb{R}^n))$.

Is the mapping \begin{equation} \begin{array}{rcl} C^0([0,T],C^1(\bar{\Omega})) & \to & L^2([0,T],H^1(\Omega))\\ \theta & \mapsto & f \circ (\mathcal{I} + \theta) \end{array} \end{equation}

continuous ?

EDIT : $\mathcal{I}$ is the identity mapping of $\mathbb{R}^n$.

Improve this question
$\endgroup$
2
  • $\begingroup$ What is $\mathcal{I}$? $\endgroup$
    – Nate Eldredge
    Commented Feb 28, 2018 at 16:31
  • $\begingroup$ $\mathcal{I}$ is the identity mapping of $\mathbb{R}^n$. Thank you for your remark, I edited the post. $\endgroup$
    – PeteAgor
    Commented Feb 28, 2018 at 16:37

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.