R. Korte

collaborators

7 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.AP2026

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 $p$ -PoincarÃ© inequality, establishing existence of solutions to Dirichlet problem in a bounde…

math.FA2026

Characterisations of Sobolev spaces and constant functions over metric spaces

Tuomas HytÃ¶nen, Riikka Korte

In a doubling metric measure space $(X, I ¨ , I^¼)$ supporting a PoincarÃ© inequality, we give a new characterisation of first-order Sobolev spaces by mean oscillations, and extend prev…

math.FA2026

Preserving Besov (fractional Sobolev) energies under sphericalization and flattening

Anders BjÃ¶rn, Jana BjÃ¶rn, Riikka Korte +2

We introduce a new sphericalization mapping for metric spaces that is applicable in very general situations, including totally disconnected fractal type sets. For an unbounded comp…

math.AP2025

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