I am trying to write the following in a mathematical notation. I have a monotonically decreasing function $V(\bullet)$, and I need to choose the argument of the function based on its amplitude.
\begin{equation} \omega_{c} = \max_{\omega} \{\omega | V(r) < 0.1 \forall r > \omega\} \end{equation}
But I want $\omega_{c}$ to be $\omega_{c}$ if it is less than or equal to $\omega_{c}^{max}$, and equal to $\omega_{c}^{max}$ otherwise.
How can I express the whole thing in a mathematical notation?
$$\omega_c = \min\left\{\max_{\omega}\{\omega | V(r) < 0.1 \forall r > \omega\}\ ,\ \omega_c^{\max} \right\}$$