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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A limiting free boundary problem ruled by Aronsson's equation


Authors: Julio D. Rossi and Eduardo V. Teixeira
Journal: Trans. Amer. Math. Soc. 364 (2012), 703-719
MSC (2010): Primary 35R35, 35J70, 62K05, 49L25
Published electronically: September 13, 2011
MathSciNet review: 2846349
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Abstract: 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.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05322-5
PII: S 0002-9947(2011)05322-5
Keywords: Optimal design, free boundary problems, infinite Laplacian
Received by editor(s): March 24, 2009
Received by editor(s) in revised form: February 9, 2010
Published electronically: September 13, 2011
Article copyright: © Copyright 2011 American Mathematical Society