A limiting free boundary problem ruled by Aronsson's equation

Details A limiting free boundary problem ruled by Aronsson's equation A limiting free boundary problem ruled by Aronsson's equation

2009-03-12

arxiv.org/abs/0903.2274v2

Mathematics

Analysis of PDEs

Scientific paper

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.

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