Ryan Gibara

collaborators

4 papers

math.AP2026

Fractional $p$ -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 $p$ -Laplace non-homogeneous equation $(- I^_{p})^{s} u = f$ , with $0 < s < 1$ , $1 < p < \infty$ , for…

math.MG2026

Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a $p$ -PoincarÃ© inequality

Sylvester Eriksson-Bique, Ryan Gibara, Riikka Korte +1

We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "…

math.AP2025

Sharp HÃ¶lder 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 HÃ¶lder regularity result for weak solutions $u \in N^{1, p} (I^c ◯, I^¼)$ to a PDE of $p$ -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\…

math.MG2025

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 $I^¼$ with $Î¼(X) = \inft…

Fractional p-Laplacians via Neumann problems in unbounded metric measure spaces

Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a p-PoincarÃ© inequality

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

On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry

Fractional $p$ -Laplacians via Neumann problems in unbounded metric measure spaces

Traces of Newton-Sobolev functions on the visible boundary of domains in doubling metric measure spaces supporting a $p$ -PoincarÃ© inequality