46 citations · 339 across the 63 of their papers we have counts for
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Homogeneous Newton-Sobolev spaces in metric measure spaces and their Banach space properties
Nageswari Shanmugalingam
In this note we prove the Banach space properties of the homogeneous Newton-Sobolev spaces of functions on an unbounded metric measure space equipped with a doubl…
Sharp Hausdorff content estimates for accessible boundaries of domains in metric measure spaces of controlled geometry
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We give a sharp Hausdorff content estimate for the size of the accessible boundary of any domain in a metric measure space of controlled geometry, i.e., a complete metric space equ…
Construction of a Dirichlet form on metric measure spaces of controlled geometry
Almaz Butaev, Liangbing Luo, Nageswari Shanmugalingam
Given a compact doubling metric measure space that supports a -Poincaré inequality, we construct a Dirichlet form on that is comparable to the upper gradient en…
Fine properties of metric space-valued mappings of bounded variation in metric measure spaces
Ivan Caamano, Josh Kline, Nageswari Shanmugalingam
Here we consider two notions of mappings of bounded variation (BV) from the metric measure space into the metric space; one based on relaxations of Newton-Sobolev functions, and th…
Discontinuous eikonal equations in metric measure spaces
Qing Liu, Nageswari Shanmugalingam, Xiaodan Zhou
In this paper, we study the eikonal equation in metric measure spaces, where the inhomogeneous term is allowed to be discontinuous, unbounded and merely -integrable in the domai…
Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a -Poincaré inequality
Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1
We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "…