A limiting free boundary problem ruled by Aronsson’s equation
Julio Daniel Rossi, Eduardo V. O. Teixeira · Transactions of the American Mathematical Society · 2011
We study the behavior of a $p$-Dirichlet optimal design problem with volume constraint for $p$ large. As the limit of $p$ goes to infinity, we find a limiting free boundary problem governed by the infinity-Laplacian operator. We find 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.