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math.FA2025
Characterisations of Sobolev spaces and constant functions over metric spaces
Tuomas Hytönen, Riikka Korte
In a doubling metric measure space supporting a Poincaré inequality, we give a new characterisation of first-order Sobolev spaces by mean oscillations, and extend previou…
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 to a PDE of -Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nab…
math.MG2025
Sharp conditions for preserving uniformity, doubling measure and Poincaré inequality under sphericalization
Riikka Korte, Sari Rogovin, Nageswari Shanmugalingam +1
We study sphericalization, which is a mapping that conformally deforms the metric and the measure of an unbounded metric measure space so that the deformed space is bounded. The go…