Continuous harmonic functions on a ball that are not in $H^s$ for $s>1/2$

Roberto Bramati, Matteo Dalla Riva, Brian Luczak

We show that there are harmonic functions on a ball ${\mathbb{B}}_n$ of ${\mathbb{R}}^n$, $n\ge 2$, that are continuous up to the boundary (and even Hölder continuous) but not in the…