In this paper we study asymptotic behavior of solutions of obstacle problems for $p-$Laplacians as $p\to \infty.$ For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of whole family of the solutions of obstacle problems either for data $f$ that change sign in $\Omega$ or for data $f$ (that do not change sign in $\Omega$) possibly vanishing in a set of positive measure.

中文翻译：

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𝑝-拉普拉斯障碍问题的极限

在本文中，我们将 $p-$Laplacians 的障碍问题解的渐近行为研究为 $p\to\infty.$ 对于一维情况和径向情况，我们给出了极限的明确表达。在 n 维情况下，我们提供了足够的条件来保证障碍问题的全族解的一致收敛，无论是对于改变符号 $\Omega$ 的数据 $f$ 还是对于数据 $f$（没有改变登录 $\Omega$) 可能在一组正度量中消失。