The set of $p$-harmonic functions in $B_1$ is total in $C^k({\bar{B}}_1)$

Abstract

Let $(-{\Delta }_p{)}^s$, with $0<s<1<p<\infty$, be the fractional $p$-Laplacian operator. We prove that the span of $p$-harmonic functions in $B_1$ is dense in $C^k({\bar{B}}_1)$.

9 pages