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

DOI:
https://doi.org/10.1090/S0002-9947-2011-05322-5

Published electronically:
September 13, 2011

MathSciNet review:
2846349

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Abstract | References | Similar Articles | Additional Information

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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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:
https://doi.org/10.1090/S0002-9947-2011-05322-5

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