On p Laplace polynomial solutions

John L. Lewis, Andrew Vogel

Abstract: We determine all real homogeneous polynomial solutions to the p Laplace equation, $-\infty < p < \infty$, $p\ne 1,2$, of degree four in $\mathbb R^n$, $n\ge 3$, and show there are no degree five real homogeneous polynomial solutions in $\mathbb R^3$ when $-\infty < p < \infty$, $p\ne 1,2$.

Journal: The Journal of Analysis

DOI: 10.1007/s41478-016-0005-6