Abstract: We study the behavior of a -Dirichlet optimal design problem with volume constraint for large. As the limit of 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.
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Julio D. Rossi Affiliation:
Departamento de Análisis Matemático, Universidad de Alicante, Alicante, Spain
Email:
jrossi@dm.uba.ar
Eduardo V. Teixeira Affiliation:
Departamento de Matemática, Universidade Federal do Ceará, Campus do Pici - Bloco 914, Fortaleza, CE - Brazil 60.455-760
Email:
eteixeira@ufc.br