In this paper we consider a closed fractal curve F, the so-called von Koch snowflake, and we construct the energy form associated to a free diffusion process on it. The main feauture is that F is not a self-similar fractal, hence it is not possible to make use of the by now well established theory of potential analysis. In order to define an energy form on F, we regard F as a fractal manifold and the energy is obtained by integrating a local energy or Lagrangian on F.
Energy form on a closed fractal curve / Lancia, Maria Rosaria; Uta Renata, Freiberg. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - STAMPA. - 23:(2004), pp. 115-137. [10.4171/zaa/1190]
Energy form on a closed fractal curve
LANCIA, Maria Rosaria;
2004
Abstract
In this paper we consider a closed fractal curve F, the so-called von Koch snowflake, and we construct the energy form associated to a free diffusion process on it. The main feauture is that F is not a self-similar fractal, hence it is not possible to make use of the by now well established theory of potential analysis. In order to define an energy form on F, we regard F as a fractal manifold and the energy is obtained by integrating a local energy or Lagrangian on F.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
