The other perspective occurs in potential theory for highly irregular domains such as fractals. The main problem then is to construct limiting diffusion operators exhibiting the self-similarities of the underlying fractal. Classical and fractal operators can be treated in a joint framework but the latter show non-classical effects in terms of scaling and fluctuations. Moreover, one would like to look for corresponding effects in time-dependent nonlinear reaction diffusion systems. The existence and uniqueness of several equations has been established on finitely ramified fractals as for example the Sierpinski gasket.
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