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We consider the doubly infinite Sierpinski gasket graph $SG_0$, rescale it byfactor $2^{-n}$, and on the rescaled graphs $SG_n=2^{-n}SG_0$, for every $n\in\mathbb{N}$, we investigate the limit shape of three aggregation models withinitial configuration $\sigma_n$ of particles supported on multiple vertices.The models under consideration are: divisible sandpile in which the excess massis distributed among the vertices until each vertex is stable and has mass lessor equal to one, internal DLA in which particles do random walks until findingan empty site, and rotor aggregation in which particles perform deterministiccounterparts of random walks until finding an empty site. We denote by$SG=cl(\cup_{n=0}^{\infty} SG_n)$ the infinite Sierpinski gasket, which is aclosed subset of $\mathbb{R}^2$, for which $SG_n$ represents the level-napproximating graph, and we consider a continuous function$\sigma:SG\to\mathbb{N}$. For $\sigma$ we solve the obstacle problem and wedescribe the noncoincidence set $D\subset SG$ as the solution of a freeboundary problem on the fractal $SG$. If the discrete particle configurations$\sigma_n$ on the approximating graphs $SG_n$ converge pointwise to thecontinuous function $\sigma$ on the limit set $SG$, we prove that, as$n\to\infty$, the scaling limits of the three aforementioned models on $SG_n$starting with initial particle configuration $\sigma_n$ converge to thedeterministic solution $D$ of the free boundary problem on the limit set$SG\subset\mathbb{R}^2$. For $D$ we also investigate boundary regularityproperties.

Internal aggregation models with multiple sources and obstacle problems on Sierpinski gaskets