I know that a mirror map $\Phi$ with respect to a norm $\|\cdot\|$ need to be strictly convex and differentiable.
For example, $$\Phi(x) = \frac{1}{2}\|x\|^2_2$$ is 1-strongly convex w.r.t. $\|\cdot\|_2$. And $$\Phi(x) = \sum_{i=1}^{n}x_i\log x_i$$ is 1-strongly convex w.r.t $\|\cdot\|_1$ on $\Delta_n$.
But how do we find a mirror map in general with respect to some norm?