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 $C^{k}(\bar{B}_{1})$.