45 citations · 146 across the 29 of their papers we have counts for
6 papers · 1 filter
Geodesic Interpolation on Sierpinski Gaskets
Caitlin M. Davis, Laura A. LeGare, Cory W. McCartan +1
We study the analogue of a convex interpolant of two sets on Sierpinski gaskets and an associated notion of measure transport. The structure of a natural family of interpolating me…
BV functions and fractional Laplacians on Dirichlet spaces
Patricia Alonso Ruiz, Fabrice Baudoin, Li Chen +3
We study Besov critical exponents and isoperimetric and Sobolev inequalities associated with fractional Laplacians on metric measure spaces. The main tool is the theory of he…
Harmonic Gradients on Higher Dimensional Sierpinski Gaskets
Luke Brown, Giovanni Ferrer, Gamal Mograby +2
We consider criteria for the differentiability of functions with continuous Laplacian on the Sierpinski Gasket and its higher-dimensional variants , , proving results th…
Spectral properties of graphs associated to the Basilica group
Antoni Brzoska, Courtney George, Samantha Jarvis +2
We provide the foundation of the spectral analysis of the Laplacian on the orbital Schreier graphs of the Basilica group, the iterated monodromy group of the quadratic polynomial $…
Besov class via heat semigroup on Dirichlet spaces III: BV functions and sub-Gaussian heat kernel estimates
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Di…
The Strong Maximum Principle for Schrödinger operators on fractals
Marius V. Ionescu, Kasso A. Okoudjou, Luke G. Rogers
We prove a strong maximum principle for Schrödinger operators defined on a class of fractal sets and their blowups without boundary. Our primary interest is in weaker regularity co…