Ryan Gibara

activity

20232025

collaborators

3 papers

math.AP2025

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 $u \in N^{1, p} (Ω, μ)$ to a PDE of $p$ -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nab…

math.AP2024

On the Dirichlet-to-Neumann Map for the $p$ -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…

math.FA2023

Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces

Ryan Gibara, Josh Kline

Let $(X, d, μ)$ be a doubling metric measure space. We consider the behaviour of the fractional maximal function $M^{α}$ for $0 \leq α < Q$ , where $Q$ is the doubling dimension, acting on…

Sharp Hölder regularity of weak solutions of the Neumann problem and applications to nonlocal PDE in metric measure spaces

On the Dirichlet-to-Neumann Map for the p-Laplacian on a Metric Measure Space

Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces

On the Dirichlet-to-Neumann Map for the $p$ -Laplacian on a Metric Measure Space