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Journal of Convex Analysis 09 (2002), No. 1, 245--258
Copyright Heldermann Verlag 2002



Nonlinear Energy Forms and Lipschitz Spaces on the Koch Curve

Raffaela Capitanelli
Dip. di Metodi e Modelli Matematici per le Scienze Applicate, UniversitÓ di Roma I, Via A. Scarpa 16, 00161 Roma, Italy
raffaela.capitanelli@uniroma1.it

Maria Rosaria Lancia
Dip. di Metodi e Modelli Matematici per le Scienze Applicate, UniversitÓ di Roma I, Via A. Scarpa 16, 00161 Roma, Italy
lancia@dmmm.uniroma1.it



[Abstract-pdf]

We consider the nonlinear convex energy forms ${\Cal E}^(p)$ on the Koch curve $K$ and we prove that the corresponding domains coincide with the spaces {\it 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.

Keywords: Nonlinear convex energy forms, fractals, Lipschitz spaces.

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