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On a Classical Spectral Optimization Problem in Linear Elasticity

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New Trends in Shape Optimization

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 166))

Abstract

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the N-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lamé and the Reissner–Mindlin systems.

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Acknowledgments

The authors acknowledge financial support from the research project ‘Singular perturbation problems for differential operators’, Progetto di Ateneo of the University of Padova. The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste, 63, 35126, Padova, Italy

    Davide Buoso & Pier Domenico Lamberti

Authors
  1. Davide Buoso
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  2. Pier Domenico Lamberti
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Correspondence to Davide Buoso .

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Editors and Affiliations

  1. Department Mathematik, Universität Erlangen‐Nürnberg, Erlangen, Germany

    Aldo Pratelli

  2. Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Günter Leugering

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Buoso, D., Lamberti, P.D. (2015). On a Classical Spectral Optimization Problem in Linear Elasticity. In: Pratelli, A., Leugering, G. (eds) New Trends in Shape Optimization. International Series of Numerical Mathematics, vol 166. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-17563-8_3

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