46 citations · 195 across the 27 of their papers we have counts for
12 papers · 1 filter
Solving Dirichlet problem on unbounded uniform domains by using sphericalization techniques
Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam +1
Within the setting of metric spaces equipped with a doubling measure and supporting a -Poincaré inequality, establishing existence of solutions to Dirichlet problem in a bounded…
Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces
Luca Capogna, Ryan Gibara, Riikka Korte +1
We prove global Hölder regularity result for weak solutions to a PDE of -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nab…
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…
Solving a Dirichlet problem for unbounded domains via a conformal transformation
Ryan Gibara, Riikka Korte, Nageswari Shanmugalingam
In this paper, we solve the -Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure s…
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…
Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry
Sylvester Eriksson-Bique, Gianmarco Giovannardi, Riikka Korte +2
We study existence, uniqueness, and regularity properties of the Dirichlet problem related to fractional Dirichlet energy minimizers in a complete doubling metric measure space $(X…