46 citations · 339 across the 63 of their papers we have counts for
6 papers · 1 filter
On Carrasco Piaggio's theorem connecting combinatorial modulus and Ahlfors regular conformal dimension
Behnam Esmayli, Ryan Schardine, Nageswari Shanmugalingam
The goal of this paper is to provide an expository description of a result of Carrasco Piaggio connecting the Ahlfors regular conformal dimension of a compact uniformly perfect dou…
Fractional -Laplacians via Neumann problems in unbounded metric measure spaces
Luca Capogna, Ryan Gibara, Riikka Korte +1
We prove well-posedness, Harnack inequality and sharp regularity of solutions to a fractional -Laplace non-homogeneous equation , with , , for d…
Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces
Takashi Kumagai, Nageswari Shanmugalingam, Ryosuke Shimizu
In the context of a metric measure space , we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of th…
Well-posedness of Dirichlet boundary value problems for reflected fractional -Laplace-type inhomogeneous equations in compact doubling metric measure spaces
Josh Kline, Feng Li, Nageswari Shanmugalingam
In this paper we consider the setting of a locally compact, non-complete metric measure space equipped with a doubling measure , under the condition that the boundary…
On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry
Ryan Gibara, Ilmari Kangasniemi, Nageswari Shanmugalingam
We study the large-scale behavior of Newton-Sobolev functions on complete, connected, proper, separable metric measure spaces equipped with a Borel measure with …
On the Dirichlet-to-Neumann Map for the -Laplacian on a Metric Measure Space
Ryan Gibara, Nageswari Shanmugalingam
In this note, we construct a Dirichlet-to-Neumann map, from a Besov space of functions, to the dual of this class. The Besov spaces are of functions on the boundary of a bounded, l…