First-order Sobolev spaces, self-similar energies and energy measures on the Sierpiński carpet

Mathav Murugan, Ryosuke Shimizu

We construct and investigate $(1,p)$-Sobolev space, $p$-energy, and the corresponding $p$-energy measures on the planar Sierpiński carpet for all $p\in (1,\infty )$. Our method…