We build a discrete stochastic process adapted to the (nonlinear) dominative $p$-Laplacian $$ \mathcal{D}_p u(x):=\Delta u + (p-2)\lambda_{N} , $$ where $\lambda_{N}$ is the largest eigenvalue of $D^2 u$ and $p > 2$. We show that the discrete solutions of the Dirichlet problems at scale $\varepsilon$ tend to the solution of the Dirichlet problem for $\mathcal{D}_p$ as $\varepsilon\to 0$. We assume that the domain and the boundary values are both Lipschitz.

中文翻译：

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支配性$ p $ -Laplacian的离散随机解释

我们建立适应（非线性）主导$ p $ -Laplacian $$ \ mathcal {D} _p u（x）：= \ Delta u +（p-2）\ lambda_ {N}，$$的离散随机过程$ \ lambda_ {N} $是$ D ^ 2 u $和$ p> 2 $的最大特征值。我们表明，尺度为\\ varepsilon $的Dirichlet问题的离散解趋向于对于$ \ mathcal {D} _p $的Dirichlet问题的解为$ \ varepsilon \至0 $。我们假设域和边界值都是Lipschitz。