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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A limiting free boundary problem ruled by Aronsson’s equation
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by Julio D. Rossi and Eduardo V. Teixeira PDF
Trans. Amer. Math. Soc. 364 (2012), 703-719 Request permission

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
  • MR Author ID: 601009
  • ORCID: 0000-0001-7622-2759
  • 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
  • MR Author ID: 710372
  • Email: eteixeira@ufc.br
  • Received by editor(s): March 24, 2009
  • Received by editor(s) in revised form: February 9, 2010
  • Published electronically: September 13, 2011
  • © Copyright 2011 American Mathematical Society
  • 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
  • MathSciNet review: 2846349