46 citations · 339 across the 63 of their papers we have counts for
7 papers · 1 filter
The Mazurkiewicz distance and sets that are finitely connected at the boundary
Anders Björn, Jana Björn, Nageswari Shanmugalingam
We study local connectedness, local accessibility and finite connectedness at the boundary, in relation to the compactness of the Mazurkiewicz completion of a bounded domain in a m…
A characterization of BMO self-maps of a metric measure space
Juha Kinnunen, Riikka Korte, Niko Marola +1
This paper studies functions of bounded mean oscillation (BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve…
Hajlasz Gradients Are Upper Gradients
Renjin Jiang, Nageswari Shanmugalingam, Dachun Yang +1
Let be a metric measure space, with a Borel regular measure. In this paper, we prove that, if and is a Hajłasz gradient…
Intrinsic Geometry and Analysis of Diffusion Processes and -Variational Problems
Pekka Koskela, Nageswari Shanmugalingam, Yuan Zhou
The aim of this paper is two-fold: First, we obtain a better understanding of the intrinsic distance of diffusion processes. Precisely, (i) for all , the diffusion matrix $A…
Geometric analysis on Cantor sets and trees
Anders Björn, Jana Björn, James T. Gill +1
Using uniformization, Cantor type sets can be regarded as boundaries of rooted trees. In this setting, we show that the trace of a first-order Sobolev space on the boundary of a re…
Boundary measures, generalized Gauss-Green formulas, and mean value property in metric measure spaces
Niko Marola, Michele Miranda, Nageswari Shanmugalingam
We study mean value properties of harmonic functions in metric measure spaces. The metric measure spaces we consider have a doubling measure and support a (1,1)- Poincaré inequalit…
The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary
Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam
In this paper we develop the Perron method for solving the Dirichlet problem for the analog of the p-Laplacian, i.e. for p-harmonic functions, with Mazurkiewicz boundary values. Th…