Joshua Kline

activity

20192023

p

-harmonic functions, and induced nonlocal operators in metric measure spaces

7 citations · 7 across the 6 of their papers we have counts for

collaborators

Showing 2022 · math.APShow all

3 papers · 2 filters

math.AP2022

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 $(1, 1)$ -Poincaré inequality, we study the problem of minimizing the BV-energy in a bounded domain $Ω$ …

math.AP2022★ 7 cited

Neumann problems for $p$ -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 $p$ -Laplacians $(- Δ_{p})^{θ}$ with $0 < θ < 1$ on any compa…

math.AP2022

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…

Obstacle problems with double boundary condition for least gradient functions in metric measure spaces

Neumann problems for p-harmonic functions, and induced nonlocal operators in metric measure spaces

Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces

Neumann problems for $p$ -harmonic functions, and induced nonlocal operators in metric measure spaces