On the non-vanishing property for real analytic solutions of the $p$-Laplace equation

Abstract

By using a nonassociative algebra argument, we prove that $u\equiv 0$ is the only cubic homogeneous polynomial solution to the $p$-Laplace equation $\mathrm{div}|Du{|}^{p-2}Du(x)=0$ in ${\mathbb{R}}^n$ for any $n\ge 2$ and $p\notin \{0,2\}$.

Submitted, 8 p

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