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Around the Research of Vladimir Maz'ya II pp 159–202Cite as

Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells

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Part of the book series: International Mathematical Series ((IMAT,volume 12))

Abstract

We consider singular perturbations of elliptic systems depending on a parameter ε such that, for ε = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro-Lopatinskii condition). The limit holds only in very abstract spaces out of distribution theory involving complexification and nonlocal phenomena. This system appears in thin shell theory when the middle surface is elliptic and the shell is fixed on a part of the boundary and free on the rest. We use a heuristic reasoning applying some simplifications which allow us to reduce the original problem in a domain to another problem on its boundary. The novelty of this work is that we consider systems of partial diferential equations while in our previous work we were dealing with single equations.

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Author information

Authors and Affiliations

  1. Laboratoire MIP, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Yuri V. Egorov

  2. Laboratoire MAP5, Université Paris Descartes (Paris V), 45 Rue des Saints Péres, 75006, Paris, France

    Nicolas Meunier

  3. Institut Jean Le Rond d’Alembert, case 162. CNRS and Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris, France

    Evariste Sanchez-Palencia

Authors
  1. Yuri V. Egorov
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  2. Nicolas Meunier
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  3. Evariste Sanchez-Palencia
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Corresponding author

Correspondence to Yuri V. Egorov .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Imperial College, Queen's Gate 180, London, SW7 2AZ, United Kingdom

    Ari Laptev

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Egorov, Y.V., Meunier, N., Sanchez-Palencia, E. (2010). Rigorous and Heuristic Treatment of Sensitive Singular Perturbations Arising in Elliptic Shells. In: Laptev, A. (eds) Around the Research of Vladimir Maz'ya II. International Mathematical Series, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1343-2_7

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