Abstract: Recent studies in analysis on fractals have established $(1, p)$-Sobolev spaces, the corresponding self-similar $p$-energy functionals and $p$-energy measures on self-similar fractals. I will present new singularity phenomena concerning these analytic objects, including the singularity of $p$-energy measures for a class of p.c.f. self-similar sets with certain geometric symmetries, as well as the mutual singularity of $(1, p)$-Sobolev spaces on the Laakso diamond space for distinct values of $p$.
This talk is based on joint works with Naotaka Kajino (Kyoto University), Riku Anttila (University of Jyväskylä), and Sylvester Eriksson-Bique (University of Jyväskylä).
Zoom Meeting ID: 181 155 584
