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