7 citations · 7 across the 6 of their papers we have counts for
6 papers
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…
Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces
Ryan Gibara, Josh Kline
Let be a doubling metric measure space. We consider the behaviour of the fractional maximal function for , where is the doubling dimension, acting on…
Obstacle problems with double boundary condition for least gradient functions in metric measure spaces
Josh Kline
In the setting of a metric space equipped with a doubling measure supporting a -Poincaré inequality, we study the problem of minimizing the BV-energy in a bounded domain …
Neumann problems for -harmonic functions, and induced nonlocal operators in metric measure spaces
Luca Capogna, Josh Kline, Riikka Korte +2
Following ideas of Caffarelli and Silvestre in~\cite{CS}, and using recent progress in hyperbolic fillings, we define fractional -Laplacians with on any compa…
Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces
Josh Kline
We study the Dirichlet problem for least gradient functions for domains in metric spaces equipped with a doubling measure and supporting a (1,1)-Poincaré inequality when the bounda…
Carathéodory-type extension theorem with respect to prime end boundaries
Joshua Kline, Jeff Lindquist, Nageswari Shanmugalingam
We prove a Carathéodory-type extension of BQS homeomorphisms between two domains in proper, locally path-connected metric spaces as homeomorphisms between their prime end closures.…