1 citations · 1 across the 8 of their papers we have counts for
10 papers
One-dimensional Dirichlet forms with prescribed Hölder regularity
Riku Anttila, Roope Anttila
We study a class of strongly local, regular Dirichlet forms on the standard unit interval. The aim of our work is to record some Hölder regularity properties that have not been not…
Cartesian products of Sierpiński carpets do not attain their conformal dimension
Riku Anttila, Sylvester Eriksson-Bique
It is a long-standing open question to determine whether the Sierpiński carpet attains its conformal dimension or not. While this problem remains unresolved, we prove that Cartesia…
Uniqueness of sign-changing solutions to Trudinger's equation
Riku Anttila, Peter Lindqvist, Mikko Parviainen
We establish uniqueness for sign-changing solutions to Trudinger's parabolic equation with time dependent Dirichlet boundary data.
Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Lassi Rainio
A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfor…
An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces
Riku Anttila
In this work, we establish a new characterization of sub-Gaussian heat kernel estimates for strongly local regular Dirichlet forms on metric measure spaces. Our formulation is base…
Sub-Gaussian heat kernel estimates for reflected diffusion on inner uniform domains
Riku Anttila
We prove that sub-Gaussian heat kernel estimates are inherited from a diffusion process on the ambient space to the reflected diffusion process on a subset which is an inner unifor…
Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces
Riku Anttila, Sylvester Eriksson-Bique, Ryosuke Shimizu
We construct self-similar -energy forms on a rich class of \emph{Laakso-type fractal spaces} and study the properties of the associated Sobolev spaces $\mathscr{…
Connections between coupling and Ishii-Lions methods for tug-of-war with noise stochastic games
Riku Anttila, Juan J. Manfredi, Mikko Parviainen
We present a streamlined account of two different regularity methods as well as their connections. We consider the coupling method in the context of tug-of-war with noise stochasti…
The Combinatorial Loewner Property and super-multiplicativity inequalities for symmetric self-similar metric spaces
Riku Anttila, Sylvester Eriksson-Bique
This paper introduces a general construction of self-similar metric spaces as limits of discrete graphs. Our framework produces many classical examples, such as the Sierpiński carp…
On Constructions of Fractal Spaces Using Replacement and the Combinatorial Loewner Property
Riku Anttila, Sylvester Eriksson-Bique
The combinatorial Loewner property was introduced by Bourdon and Kleiner as a quasisymmetrically invariant substitute for the Loewner property for general fractals and boundaries o…