Nonlinear Energy Forms and Lipschitz Spaces on the Koch Curve

We consider the nonlinear convex energy forms $\mathcal{E}^{(p)}$ on the Koch curve $K$ and we prove that the corresponding domains coincide with the spaces $\mathit{Lip}_{\alpha, D_f} (p, \infty, K)$. Then we give a precise interpretation of the smoothness index $\alpha$ in terms of the structural constants of the fractal.