一个由Aronsson方程控制的极限自由边界问题
A limiting free boundary problem ruled by Aronsson's equation
摘要：
本文研究了$p$大容量下带体积约束的$p$ -Dirichlet最优设计问题的性质。当$p$的极限趋于无穷大时，我们发现一个由无穷大拉普拉斯算子控制的极限自由边界问题。我们建立了极限问题唯一性的充要条件，并在此条件下精确地确定了极限问题的最优配置。最后，我们建立了自由边界的收敛结果。
英文摘要：
We study the behavior of $p$-Dirichlet optimal design problem with volume constraint for $p$ large. As the limit as $p$ goes to infinity, we find a limiting free boundary problem governed by the infinity-Laplacian operator. We establish a necessary and sufficient condition for uniqueness of the limiting problem and, under such a condition, we determine precisely the optimal configuration for the limiting problem. Finally, we establish convergence results for the free boundaries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
