5 citations · 11 across the 9 of their papers we have counts for
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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…
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…
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…