We consider the interior Hölder regularity of spatial gradient viscosity solution to parabolic normalized p ( x , t ) -Laplace equation u = ? i j + ? 2 | D with some suitable assumptions on which arises naturally from a two-player zero-sum stochastic differential game probabilities depending space and time.

In this note we prove the nonexistence of stable solutions to the p-Laplace equation −∆pu = eu on the entire Euclidean space RN , where p > 2 and N < p(p+3) p−1 .

By using a nonassociative algebra argument, we prove that u ≡ 0 is the only cubic homogeneous polynomial solution to the p-Laplace equation div|Du|p−2Du(x) = 0 in Rn for any n ≥ 2 and p 6∈ {1, 2}.