compare SVR with medium regression

We usually compare Supporting vector regression (SVR): $$\mathcal{L} = C\sum\limits_{n=1}^{N}\Big(|y_i - g(x_i)| - \epsilon\Big)^+ + \dfrac{1}{2}||w||^2.$$ and ridge regression (RR): $$\mathcal{L} = \sum\limits_{n=1}^{N}\Big(y_i - g(x_i)\Big)^2 + \dfrac{1}{2}||w||^2.$$ Here the fitting line is: $$g(x_i) = wx_i + b.$$

Since they both have $L_2$ Regularization and both can apply the Kernel trick.

But I am very surprised that I cannot find any reference about SVR and medium regression with $L_2$ Regularization: $$\mathcal{L} = C\sum\limits_{n=1}^{N}\Big(|y_i - g(x_i)|\Big) + \dfrac{1}{2}||w||^2.$$ which is just the SVR with $\epsilon = 0.$

Do you know any story about their relation?