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The N-membranes Problem with Neumann Type Boundary Condition

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Free Boundary Problems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 154))

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Abstract

We consider the problem of finding the equilibrium position of N membranes constrained not to pass through each other, under prescribed volumic forces and boundary tensions. This model corresponds to solve variationally a N-system for linear second order elliptic equations with sequential constraints. We obtain interior and boundary Lewy-Stampacchia type inequalities for the respective solution and we establish the conditions for stability in measure of the interior contact zones of the membranes.

This work was partially supported by FCT (Fundação para a Ciência e Tecnologia).

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References

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Author information

Authors and Affiliations

  1. University of Minho, Campus de Gualtar, 4700-030, Braga, Portugal

    A. Azevedo & L. Santos

  2. CMUC/University of Coimbra and University of Lisbon, Av. Prof. Gama Pinto, 2, 1649-003, Lisboa, Portugal

    J. F. Rodrigues

Authors
  1. A. Azevedo
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  2. J. F. Rodrigues
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  3. L. Santos
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Editor information

Editors and Affiliations

  1. Departamento de Matemática Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal

    Isabel Narra Figueiredo

  2. Universidade de Lisboa / CMAF, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    José Francisco Rodrigues

  3. Departamento de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Lisa Santos

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Azevedo, A., Rodrigues, J.F., Santos, L. (2006). The N-membranes Problem with Neumann Type Boundary Condition. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_6

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