We investigate the limiting behavior of solutions to the inhomogeneous p-Laplacian equation \(-\Delta _{p} u = \mu _{p}\) subject to Neumann boundary conditions. For right-hand sides, which are arbitrary signed measures, we show that solutions converge to a Kantorovich potential associated with the geodesic Wasserstein-1 distance. In the regular case with continuous right-hand sides, we characterize the limit as viscosity solution to an infinity Laplacian / eikonal type equation.

中文翻译：

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具有 Neumann 边界条件的非齐次 p-Laplacian 方程在极限 $p\to \infty $

我们研究了受诺伊曼边界条件影响的非齐次p -拉普拉斯方程\(-\Delta _{p} u = \mu _{p}\)的解的极限行为。对于右侧，这是任意带符号的措施，我们表明解决方案收敛到与测地线 Wasserstein-1 距离相关的 Kantorovich 势能。在右侧连续的常规情况下，我们将极限描述为无穷拉普拉斯算子/eikonal 型方程的粘度解。