The Dominative $p$-Laplacian is the operator defined for $2\le p < \infty$ as follows: \begin{ equation}\label{ dominativep} \mathcal{ L}_{ p}u(x)=\frac{ 1}{ p}\left(\lambda_{ 1}+\ldots+\lambda_{ N-1}\right)+\frac{ (p-1)}{ p}\lambda_{ N}, \end{ equation} where we have ordered the eigenvalues of $D^{ 2}u(x)$ as $\lambda_{ 1}\le \lambda_{ 2}\ldots\le\lambda_{ N}$. The operator $\mathcal{ L}_{ p}u(x)$ was introduced by Brustand to give a natural explanation of the superposition principle for the $p$-Laplace equation. In this paper, we present a discrete stochastic approximation to the unique viscosity solution of the Dirichlet problem for the Dominative $p$-Laplace Equation.
Categories: math.AP