Linear relations for \(p\)-harmonic functions (Q2462356)

For \(p\neq 2\), \(p\)-harmonic functions in \(\mathbb R^n\) do not form a linear space. In spite of this, the author is able to show that for some \(n\)-harmonic functions \(u\) and \(v\) also \(u-v\) is \(n\)-harmonic. It is also shown that for the \(n\)-harmonic functions \(u_j(x)= x_j /| x| ^2, j=1,\dots,n,\) and for all \(a_j\in \mathbb R\) the function \(\sum_{j=1}^n a_j u_j\) is \(n\)-harmonic.