A Spectral Triple for a Solenoid Based on the Sierpinski Gasket

Sampling on the Sierpinski Gasket

Interacting dimers on a Sierpinski gasket

The different manners of embedding subgraphs of many disjoint edges in a parent graph arise in several different chemical and physical contexts. The problem of enumeration, or more generally of weighted summation, of such embeddings seems quite difficult to treat quantitatively, at least for general extended graphs. The special extended parent graph treated here with the inclusion of interactio...

A note on elliptic problems on the Sierpinski gasket

Using a method that goes back to J. Saint Raymond, we prove the existence of infinitely many weak solutions of certain nonlinear elliptic problems defined on the SG. Mathematics Subject Classification (2010): 35J20, 28A80, 35J25, 35J60, 47J30, 49J52.

Generalized eigenfunctions and a Borel Theorem on the Sierpinski Gasket.∗

There is a well developed theory (see [5, 9]) of analysis on certain types of fractal sets, of which the Sierpinski Gasket (SG) is the simplest non-trivial example. In this theory the fractals are viewed as limits of graphs, and notions analogous to the Dirichlet energy and the Laplacian are constructed as renormalized limits of the corresponding objects on the approximating graphs. The nature ...

Hölder extension of a function defined on a Sierpinski gasket

We construct a linear extension operator Π that extends a function u defined on a Sierpinski gasket S which satisfies the Hölder estimate |u(x)− u(y)| ≤ C0|x− y| for all x, y on S, to a larger domain Ω ⊆ R. The extension function Πu is defined everywhere in Ω, is Hölder continuous everywhere in Ω, corresponds with u at every point on S and satisfies the estimate |Πu|Ω,β ≤ C‖u‖S,β with a constan...