The laplacian of the hany fractal

Abstract EN

Heat conduction on fractals might provide some insight into continuous transport phenomena on porous media.

Therefore we identify the generator of the heat semigroup, the “Laplacian,” of the Hany fractal.

This fractal is finitely ramified and graph-directed.

The standard existence and uniqueness criteria of Lindstrøm, Sabot, and the author do not apply to it [1].

Thus it might become a kind of benchmark test for future abstract existence and/or uniqueness criteria.

Techniques related to self-similar electrical resistor networks (symmetric Dirichlet forms) and nonlinear Perron–Frobenius theory are employed.