Using Self-adjoint Extensions in Shape Optimization

  • Antoine Laurain
  • Katarzyna Szulc
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 312)


Self-adjoint extensions of elliptic operators are used to model the solution of a partial differential equation defined in a singularly perturbed domain. The asymptotic expansion of the solution of a Laplacian with respect to a small parameter ε is first performed in a domain perturbed by the creation of a small hole. The resulting singular perturbation is approximated by choosing an appropriate self-adjoint extension of the Laplacian, according to the previous asymptotic analysis. The sensitivity with respect to the position of the center of the small hole is then studied for a class of functionals depending on the domain. A numerical application for solving an inverse problem is presented. Error estimates are provided and a link to the notion of topological derivative is established.


Asymptotic Analysis Elliptic Operator Small Hole Shape Optimization Singular Perturbation 
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Copyright information

© IFIP International Federation for Information Processing 2009

Authors and Affiliations

  • Antoine Laurain
    • 1
  • Katarzyna Szulc
    • 2
  1. 1.Department of Mathematics and Scientific ComputingUniversity of GrazGrazAustria
  2. 2.Institut Élie CartanUniversity Henri PoincaréNancy1France

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